Edit after second review

Author: jonasteuwen

Teuwen-GaussianMF.bbl

@@ -18,30 +18,33 @@ E.~M. Stein, Harmonic analysis: real-variable methods, orthogonality, and
   University Press, Princeton, NJ, 1993, with the assistance of Timothy S.
   Murphy, Monographs in Harmonic Analysis, III.
 
-\bibitem{MaasNeervenPortal2011b}
-J.~Maas, J.~van Neerven, P.~Portal,
-  \href{http://projecteuclid.org/euclid.pm/1308748950
-  http://arxiv.org/abs/1003.4092}{{Non-tangential maximal functions and conical
-  square functions with respect to the Gaussian measure}}, Publicacions
-  Matem\`{a}tiques 55~(2) (2010) 21.
-\newblock \href {http://arxiv.org/abs/1003.4092} {\path{arXiv:1003.4092}}.
-\newline\urlprefix\url{http://projecteuclid.org/euclid.pm/1308748950
-  http://arxiv.org/abs/1003.4092}
+\bibitem{Mattila1995}
+P.~Mattila, {Geometry of Sets and Measures in Euclidean Spaces}, Cambridge
+  University Press, Cambridge, 1995.
+\newblock \href {http://dx.doi.org/10.1017/CBO9780511623813}
+  {\path{doi:10.1017/CBO9780511623813}}.
+
+\bibitem{Liliana2002}
+F.~Liliana, S.~Roberto, S.~Peter, U.~Wilfredo, {On the $L^p$ boundedness of the
+  non-centered Gaussian Hardy-Littlewood maximal function}, Proceedings of the
+  American Mathematical Society 130~(1) (2002) 73--79.
+\newblock \href {http://dx.doi.org/10.1090/S0002-9939-01-06156-1}
+  {\path{doi:10.1090/S0002-9939-01-06156-1}}.
 
 \bibitem{Portal2014}
 P.~Portal, {Maximal and quadratic Gaussian Hardy spaces}, Revista
   Matem\'{a}tica Iberoamericana 30~(1), to appear (2014).
 
 \bibitem{Sjogren1997}
 P.~Sj\"{o}gren, \href{http://link.springer.com/10.1007/BF02656487}{{Operators
-  associated with the hermite semigroup -- a survey}}, The Journal of Fourier
+  associated with the Hermite semigroup -- a survey}}, The Journal of Fourier
   Analysis and Applications 3~(S1) (1997) 813--823.
 \newblock \href {http://dx.doi.org/10.1007/BF02656487}
   {\path{doi:10.1007/BF02656487}}.
 \newline\urlprefix\url{http://link.springer.com/10.1007/BF02656487}
 
 \bibitem{MaasNeervenPortal2011}
-J.~Maas, J.~Neerven, P.~Portal, {Whitney coverings and the tent spaces
+J.~Maas, J.~van Neerven, P.~Portal, {Whitney coverings and the tent spaces
   $T^{1,q}(\gamma)$ for the Gaussian measure}, Arkiv f\"{o}r Matematik 50~(2)
   (2011) 379--395.
 \newblock \href {http://dx.doi.org/10.1007/s11512-010-0143-z}

Teuwen-GaussianMF.bib

@@ -1,6 +1,6 @@
 @article{MaasNeervenPortal2011,
 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.},
-author = {Maas, Jan and Neerven, Jan and Portal, Pierre},
+author = {Maas, Jan and van Neerven, Jan and Portal, Pierre},
 doi = {10.1007/s11512-010-0143-z},
 issn = {0004-2080},
 journal = {Arkiv f\"{o}r Matematik},
@@ -27,7 +27,7 @@ @article{MaasNeervenPortal2011b
 pages = {21},
 publisher = {Universitat Aut\`{o}noma de Barcelona, Departament de Matem\`{a}tiques},
 title = {{Non-tangential maximal functions and conical square functions with respect to the Gaussian measure}},
-url = {http://projecteuclid.org/euclid.pm/1308748950 http://arxiv.org/abs/1003.4092},
+url = {http://projecteuclid.org/euclid.pm/1308748950},
 volume = {55},
 year = {2010}
 }
@@ -68,7 +68,7 @@ @article{Sjogren1997
 number = {S1},
 pages = {813--823},
 publisher = {Birkh\"{a}user Boston},
-title = {{Operators associated with the hermite semigroup -- a survey}},
+title = {{Operators associated with the Hermite semigroup -- a survey}},
 url = {http://link.springer.com/10.1007/BF02656487},
 volume = {3},
 year = {1997}
@@ -105,4 +105,29 @@ @book {Stein1993
    MRCLASS = {42-02 (35Sxx 43-02 47G30)},
   MRNUMBER = {1232192 (95c:42002)},
 MRREVIEWER = {Michael Cowling},
-}
+}
+
+
+@book{Mattila1995,
+address = {Cambridge},
+author = {Mattila, Pertti},
+doi = {10.1017/CBO9780511623813},
+isbn = {9780511623813},
+pmid = {3487781},
+publisher = {Cambridge University Press},
+title = {{Geometry of Sets and Measures in Euclidean Spaces}},
+year = {1995}
+}
+
+
+@article{Liliana2002,
+author = {Liliana, Forzani and Roberto, Scotto and Peter, Sj\"ogren and Wilfredo, Urbina},
+doi = {10.1090/S0002-9939-01-06156-1},
+journal = {Proceedings of the American Mathematical Society},
+mendeley-groups = {Mathematics},
+number = {1},
+pages = {73--79},
+title = {{On the $L^p$ boundedness of the non-centered Gaussian Hardy-Littlewood maximal function}},
+volume = {130},
+year = {2002}
+}

Teuwen-GaussianMF.bib~

@@ -0,0 +1,120 @@
+@article{MaasNeervenPortal2011,
+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.},
+author = {Maas, Jan and van Neerven, Jan and Portal, Pierre},
+doi = {10.1007/s11512-010-0143-z},
+issn = {0004-2080},
+journal = {Arkiv f\"{o}r Matematik},
+keywords = {Gaussian,Mathematics and Statistics,Whitney,measure,tent},
+month = apr,
+number = {2},
+pages = {379--395},
+publisher = {Springer Netherlands},
+title = {{Whitney coverings and the tent spaces $T^{1,q}(\gamma)$ for the Gaussian measure}},
+volume = {50},
+year = {2011}
+}
+
+@article{MaasNeervenPortal2011b,
+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.},
+archivePrefix = {arXiv},
+arxivId = {1003.4092},
+author = {Maas, Jan and van Neerven, Jan and Portal, Pierre},
+eprint = {1003.4092},
+journal = {Publicacions Matem\`{a}tiques},
+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},
+month = mar,
+number = {2},
+pages = {21},
+publisher = {Universitat Aut\`{o}noma de Barcelona, Departament de Matem\`{a}tiques},
+title = {{Non-tangential maximal functions and conical square functions with respect to the Gaussian measure}},
+url = {http://projecteuclid.org/euclid.pm/1308748950},
+volume = {55},
+year = {2010}
+}
+
+@article{Pineda2008,
+author = {Pineda, Ebner and Urbina, Wilfredo R.},
+issn = {1315-2068},
+journal = {Divulgaciones Matem\'{a}ticas},
+keywords = {hermite expansions,non tangential convergence,ornstein-uhlenbeck,poisson-hermite semigroup,uhlenbeck semigroup},
+number = {2},
+pages = {1--19},
+title = {{Non Tangential Convergence for the Ornstein-Uhlenbeck Semigroup}},
+url = {http://www.emis.ams.org/journals/DM/v16-1/art7.pdf},
+volume = {13},
+year = {2008}
+}
+
+@article{Portal2014,
+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.},
+author = {Portal, Pierre},
+journal = {Revista Matem\'{a}tica Iberoamericana},
+title = {{Maximal and quadratic Gaussian Hardy spaces}},
+number = {1},
+volume = {30},
+keywords = {Hardy,gaussian,ornstein,uhlenbeck},
+month = mar,
+year = {2014},
+note = {To appear (2014)}
+}
+
+@article{Sjogren1997,
+author = {Sj\"{o}gren, Peter},
+doi = {10.1007/BF02656487},
+issn = {1069-5869},
+journal = {The Journal of Fourier Analysis and Applications},
+keywords = {hermite,ornstein-uhlenbeck},
+month = jan,
+number = {S1},
+pages = {813--823},
+publisher = {Birkh\"{a}user Boston},
+title = {{Operators associated with the Hermite semigroup -- a survey}},
+url = {http://link.springer.com/10.1007/BF02656487},
+volume = {3},
+year = {1997}
+}
+
+@article{Mauceri2007,
+author = {Mauceri, Giancarlo and Meda, Stefano},
+doi = {10.1016/j.jfa.2007.06.017},
+issn = {00221236},
+journal = {Journal of Functional Analysis},
+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},
+month = nov,
+number = {1},
+pages = {278--313},
+title = {{BMO and $H^1$ for the Ornstein–Uhlenbeck operator}},
+url = {http://linkinghub.elsevier.com/retrieve/pii/S0022123607002613},
+volume = {252},
+year = {2007}
+}
+
+@book {Stein1993,
+    AUTHOR = {Stein, Elias M.},
+     TITLE = {Harmonic analysis: real-variable methods, orthogonality, and
+              oscillatory integrals},
+    SERIES = {Princeton Mathematical Series},
+    VOLUME = {43},
+      NOTE = {With the assistance of Timothy S. Murphy,
+              Monographs in Harmonic Analysis, III},
+ PUBLISHER = {Princeton University Press},
+   ADDRESS = {Princeton, NJ},
+      YEAR = {1993},
+     PAGES = {xiv+695},
+      ISBN = {0-691-03216-5},
+   MRCLASS = {42-02 (35Sxx 43-02 47G30)},
+  MRNUMBER = {1232192 (95c:42002)},
+MRREVIEWER = {Michael Cowling},
+}
+
+
+@book{Mattila1995,
+address = {Cambridge},
+author = {Mattila, Pertti},
+doi = {10.1017/CBO9780511623813},
+isbn = {9780511623813},
+pmid = {3487781},
+publisher = {Cambridge University Press},
+title = {{Geometry of Sets and Measures in Euclidean Spaces}},
+year = {1995}
+}