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Copy file name to clipboardExpand all lines: Teuwen-GaussianMF.bib
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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}},
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.},
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},
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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}},
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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