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Teuwen-GaussianMF.bbl

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@@ -12,13 +12,29 @@ E.~Pineda, W.~R. Urbina,
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Matem\'{a}ticas 13~(2) (2008) 1--19.
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\newline\urlprefix\url{http://www.emis.ams.org/journals/DM/v16-1/art7.pdf}
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\bibitem{Stein1993}
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E.~M. Stein, Harmonic analysis: real-variable methods, orthogonality, and
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oscillatory integrals, Vol.~43 of Princeton Mathematical Series, Princeton
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University Press, Princeton, NJ, 1993, with the assistance of Timothy S.
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Murphy, Monographs in Harmonic Analysis, III.
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\bibitem{MaasNeervenPortal2011b}
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J.~Maas, J.~van Neerven, P.~Portal,
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\href{http://projecteuclid.org/euclid.pm/1308748950
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http://arxiv.org/abs/1003.4092}{{Non-tangential maximal functions and conical
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square functions with respect to the Gaussian measure}}, Publicacions
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Matem\`{a}tiques 55~(2) (2010) 21.
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\newblock \href {http://arxiv.org/abs/1003.4092} {\path{arXiv:1003.4092}}.
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\newline\urlprefix\url{http://projecteuclid.org/euclid.pm/1308748950
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http://arxiv.org/abs/1003.4092}
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\bibitem{Portal2014}
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P.~Portal, {Maximal and quadratic Gaussian Hardy spaces}, Revista
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Matem\'{a}ticas Iberoamericana 30~(1), to appear (2014).
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Matem\'{a}tica Iberoamericana 30~(1), to appear (2014).
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\bibitem{Sjogren1997}
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P.~Sj\"{o}gren, \href{http://link.springer.com/10.1007/BF02656487}{{Operators
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associated with the hermite semigroup -- A survey}}, The Journal of Fourier
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associated with the hermite semigroup -- a survey}}, The Journal of Fourier
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Analysis and Applications 3~(S1) (1997) 813--823.
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\newblock \href {http://dx.doi.org/10.1007/BF02656487}
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{\path{doi:10.1007/BF02656487}}.
@@ -31,4 +47,13 @@ J.~Maas, J.~Neerven, P.~Portal, {Whitney coverings and the tent spaces
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\newblock \href {http://dx.doi.org/10.1007/s11512-010-0143-z}
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{\path{doi:10.1007/s11512-010-0143-z}}.
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\bibitem{Mauceri2007}
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G.~Mauceri, S.~Meda,
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\href{http://linkinghub.elsevier.com/retrieve/pii/S0022123607002613}{{BMO and
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$H^1$ for the Ornstein–Uhlenbeck operator}}, Journal of Functional Analysis
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252~(1) (2007) 278--313.
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\newblock \href {http://dx.doi.org/10.1016/j.jfa.2007.06.017}
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{\path{doi:10.1016/j.jfa.2007.06.017}}.
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\newline\urlprefix\url{http://linkinghub.elsevier.com/retrieve/pii/S0022123607002613}
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\end{thebibliography}

Teuwen-GaussianMF.bib

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@@ -14,6 +14,24 @@ @article{MaasNeervenPortal2011
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year = {2011}
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}
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@article{MaasNeervenPortal2011b,
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abstract = {We study, in \$L\^{}\{1\}(\backslash R\^{}n;\backslash gamma)\$ with respect to the gaussian measure, non-tangential maximal functions and conical square functions associated with the Ornstein-Uhlenbeck operator by developing a set of techniques which allow us, to some extent, to compensate for the non-doubling character of the gaussian measure. The main result asserts that conical square functions can be controlled in \$L\^{}1\$-norm by non-tangential maximal functions. Along the way we prove a change of aperture result for the latter. This complements recent results on gaussian Hardy spaces due to Mauceri and Meda.},
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archivePrefix = {arXiv},
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arxivId = {1003.4092},
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author = {Maas, Jan and van Neerven, Jan and Portal, Pierre},
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eprint = {1003.4092},
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journal = {Publicacions Matem\`{a}tiques},
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keywords = {and phrases,ganisation for scientific research,gaussian measure,hardy spaces,is supported by rubicon,is supported by vici,maximal function,netherlands or-,nwo,ornstein-uhlenbeck operator,square function,subsidy,subsidy 680-50-0901 of the,the first named author,the second named author},
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month = mar,
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number = {2},
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pages = {21},
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publisher = {Universitat Aut\`{o}noma de Barcelona, Departament de Matem\`{a}tiques},
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title = {{Non-tangential maximal functions and conical square functions with respect to the Gaussian measure}},
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url = {http://projecteuclid.org/euclid.pm/1308748950 http://arxiv.org/abs/1003.4092},
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volume = {55},
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year = {2010}
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}
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@article{Pineda2008,
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author = {Pineda, Ebner and Urbina, Wilfredo R.},
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issn = {1315-2068},
@@ -30,7 +48,7 @@ @article{Pineda2008
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@article{Portal2014,
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abstract = {Building on the author's recent work with Jan Maas and Jan van Neerven, this paper establishes the equivalence of two norms (one using a maximal function, the other a square function) used to define a Hardy space on $\R^{n}$ with the gaussian measure, that is adapted to the Ornstein-Uhlenbeck semigroup. In contrast to the atomic Gaussian Hardy space introduced earlier by Mauceri and Meda, the $h^{1}(\R^{n};d\gamma)$ space studied here is such that the Riesz transforms are bounded from $h^{1}(\R^{n};d\gamma)$ to $L^{1}(\R^{n};d\gamma)$. This gives a gaussian analogue of the seminal work of Fefferman and Stein in the case of the Lebesgue measure and the usual Laplacian.},
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author = {Portal, Pierre},
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journal = {Revista Matem\'{a}ticas Iberoamericana},
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journal = {Revista Matem\'{a}tica Iberoamericana},
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title = {{Maximal and quadratic Gaussian Hardy spaces}},
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number = {1},
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volume = {30},
@@ -50,8 +68,41 @@ @article{Sjogren1997
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number = {S1},
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pages = {813--823},
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publisher = {Birkh\"{a}user Boston},
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title = {{Operators associated with the hermite semigroup -- A survey}},
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title = {{Operators associated with the hermite semigroup -- a survey}},
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url = {http://link.springer.com/10.1007/BF02656487},
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volume = {3},
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year = {1997}
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}
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@article{Mauceri2007,
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author = {Mauceri, Giancarlo and Meda, Stefano},
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doi = {10.1016/j.jfa.2007.06.017},
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issn = {00221236},
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journal = {Journal of Functional Analysis},
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keywords = {a,analisi armonica,analisi tempo-frequenza e,and the progetto cofinanziato,atomic hardy space,bmo,corresponding author,gauss measure,imaginary powers,laplaciani generalizzati,m,n,p,prin2005,project,riesz transform,singular integrals,teoria delle rappresentazioni,the italian g,work partially supported by},
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month = nov,
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number = {1},
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pages = {278--313},
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title = {{BMO and $H^1$ for the Ornstein–Uhlenbeck operator}},
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url = {http://linkinghub.elsevier.com/retrieve/pii/S0022123607002613},
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volume = {252},
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year = {2007}
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}
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@book {Stein1993,
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AUTHOR = {Stein, Elias M.},
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TITLE = {Harmonic analysis: real-variable methods, orthogonality, and
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oscillatory integrals},
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SERIES = {Princeton Mathematical Series},
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VOLUME = {43},
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NOTE = {With the assistance of Timothy S. Murphy,
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Monographs in Harmonic Analysis, III},
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PUBLISHER = {Princeton University Press},
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ADDRESS = {Princeton, NJ},
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YEAR = {1993},
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PAGES = {xiv+695},
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ISBN = {0-691-03216-5},
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MRCLASS = {42-02 (35Sxx 43-02 47G30)},
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MRNUMBER = {1232192 (95c:42002)},
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MRREVIEWER = {Michael Cowling},
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}

Teuwen-GaussianMF.bib~

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@@ -0,0 +1,108 @@
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@article{MaasNeervenPortal2011,
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abstract = {We introduce a technique for handling Whitney decompositions in Gaussian harmonic analysis and apply it to the study of Gaussian analogues of the classical tent spaces $T^{1, q}$ of Coifman–Meyer–Stein.},
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author = {Maas, Jan and Neerven, Jan and Portal, Pierre},
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doi = {10.1007/s11512-010-0143-z},
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issn = {0004-2080},
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journal = {Arkiv f\"{o}r Matematik},
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keywords = {Gaussian,Mathematics and Statistics,Whitney,measure,tent},
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month = apr,
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number = {2},
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pages = {379--395},
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publisher = {Springer Netherlands},
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title = {{Whitney coverings and the tent spaces $T^{1,q}(\gamma)$ for the Gaussian measure}},
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volume = {50},
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year = {2011}
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}
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@article{MaasNeervenPortal2011b,
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abstract = {We study, in \$L\^{}\{1\}(\backslash R\^{}n;\backslash gamma)\$ with respect to the gaussian measure, non-tangential maximal functions and conical square functions associated with the Ornstein-Uhlenbeck operator by developing a set of techniques which allow us, to some extent, to compensate for the non-doubling character of the gaussian measure. The main result asserts that conical square functions can be controlled in \$L\^{}1\$-norm by non-tangential maximal functions. Along the way we prove a change of aperture result for the latter. This complements recent results on gaussian Hardy spaces due to Mauceri and Meda.},
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archivePrefix = {arXiv},
20+
arxivId = {1003.4092},
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author = {Maas, Jan and van Neerven, Jan and Portal, Pierre},
22+
eprint = {1003.4092},
23+
journal = {Publicacions Matem\`{a}tiques},
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keywords = {and phrases,ganisation for scientific research,gaussian measure,hardy spaces,is supported by rubicon,is supported by vici,maximal function,netherlands or-,nwo,ornstein-uhlenbeck operator,square function,subsidy,subsidy 680-50-0901 of the,the first named author,the second named author},
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month = mar,
26+
number = {2},
27+
pages = {21},
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publisher = {Universitat Aut\`{o}noma de Barcelona, Departament de Matem\`{a}tiques},
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title = {{Non-tangential maximal functions and conical square functions with respect to the Gaussian measure}},
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url = {http://projecteuclid.org/euclid.pm/1308748950 http://arxiv.org/abs/1003.4092},
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volume = {55},
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year = {2010}
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}
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@article{Pineda2008,
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author = {Pineda, Ebner and Urbina, Wilfredo R.},
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issn = {1315-2068},
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journal = {Divulgaciones Matem\'{a}ticas},
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keywords = {hermite expansions,non tangential convergence,ornstein-uhlenbeck,poisson-hermite semigroup,uhlenbeck semigroup},
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number = {2},
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pages = {1--19},
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title = {{Non Tangential Convergence for the Ornstein-Uhlenbeck Semigroup}},
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url = {http://www.emis.ams.org/journals/DM/v16-1/art7.pdf},
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volume = {13},
45+
year = {2008}
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}
47+
48+
@article{Portal2014,
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abstract = {Building on the author's recent work with Jan Maas and Jan van Neerven, this paper establishes the equivalence of two norms (one using a maximal function, the other a square function) used to define a Hardy space on $\R^{n}$ with the gaussian measure, that is adapted to the Ornstein-Uhlenbeck semigroup. In contrast to the atomic Gaussian Hardy space introduced earlier by Mauceri and Meda, the $h^{1}(\R^{n};d\gamma)$ space studied here is such that the Riesz transforms are bounded from $h^{1}(\R^{n};d\gamma)$ to $L^{1}(\R^{n};d\gamma)$. This gives a gaussian analogue of the seminal work of Fefferman and Stein in the case of the Lebesgue measure and the usual Laplacian.},
50+
author = {Portal, Pierre},
51+
journal = {Revista Matem\'{a}tica Iberoamericana},
52+
title = {{Maximal and quadratic Gaussian Hardy spaces}},
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number = {1},
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volume = {30},
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keywords = {Hardy,gaussian,ornstein,uhlenbeck},
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month = mar,
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year = {2014},
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note = {To appear (2014)}
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}
60+
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@article{Sjogren1997,
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author = {Sj\"{o}gren, Peter},
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doi = {10.1007/BF02656487},
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issn = {1069-5869},
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journal = {The Journal of Fourier Analysis and Applications},
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keywords = {hermite,ornstein-uhlenbeck},
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month = jan,
68+
number = {S1},
69+
pages = {813--823},
70+
publisher = {Birkh\"{a}user Boston},
71+
title = {{Operators associated with the hermite semigroup -- A survey}},
72+
url = {http://link.springer.com/10.1007/BF02656487},
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volume = {3},
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year = {1997}
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}
76+
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@article{Mauceri2007,
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author = {Mauceri, Giancarlo and Meda, Stefano},
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doi = {10.1016/j.jfa.2007.06.017},
80+
issn = {00221236},
81+
journal = {Journal of Functional Analysis},
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keywords = {a,analisi armonica,analisi tempo-frequenza e,and the progetto cofinanziato,atomic hardy space,bmo,corresponding author,gauss measure,imaginary powers,laplaciani generalizzati,m,n,p,prin2005,project,riesz transform,singular integrals,teoria delle rappresentazioni,the italian g,work partially supported by},
83+
month = nov,
84+
number = {1},
85+
pages = {278--313},
86+
title = {{BMO and \$H\^{}1\$ for the Ornstein–Uhlenbeck operator}},
87+
url = {http://linkinghub.elsevier.com/retrieve/pii/S0022123607002613},
88+
volume = {252},
89+
year = {2007}
90+
}
91+
92+
@book {Stein1993,
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AUTHOR = {Stein, Elias M.},
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TITLE = {Harmonic analysis: real-variable methods, orthogonality, and
95+
oscillatory integrals},
96+
SERIES = {Princeton Mathematical Series},
97+
VOLUME = {43},
98+
NOTE = {With the assistance of Timothy S. Murphy,
99+
Monographs in Harmonic Analysis, III},
100+
PUBLISHER = {Princeton University Press},
101+
ADDRESS = {Princeton, NJ},
102+
YEAR = {1993},
103+
PAGES = {xiv+695},
104+
ISBN = {0-691-03216-5},
105+
MRCLASS = {42-02 (35Sxx 43-02 47G30)},
106+
MRNUMBER = {1232192 (95c:42002)},
107+
MRREVIEWER = {Michael Cowling},
108+
}

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