@article{6c9407e445204b209cecd8e9d73aca59,
title = "Hardy spaces and the Tb theorem",
abstract = "It is well-known that Calder{\'o}n-Zygmund operators T are bounded on H p for n/n+1 < p ≤ 1 provided T*(1) = 0. In this article, it is shown that if T*(b) = 0, where b is a para-accretive function, T is bounded from the classical Hardy space H p to a new Hardy space H b p . To develop an H b p theory, a discrete Calder{\'o}n-type reproducing formula and Plancherel-P{\^o}lya- type inequalities associated to a para-accretive function are established. Moreover, David, Journ{\'e}, and Semmes' result [9] about the L P, 1 < p < ∞, boundedness of the Littlewood-Paley g function associated to a para-accretive function is generalized to the case of p ≤ 1. A new characterization of the classical Hardy spaces by using more general cancellation adapted to para-accretive functions is also given. These results complement the celebrated Calder{\'o}n-Zygmund operator theory.",
keywords = "Calder{\'o}n-Zygmund operator, Hardy space, Littlewood-Paley g function, Plancherel-Pl{\^o}ya inequality, Tb theorem, discrete Calder{\'o}n formula",
author = "Yongsheng Han and Lee, {Ming Yi} and Lin, {Chin Cheng}",
note = "Funding Information: Math Subject Classifications. 42B25, 42B30. Key Words and Phrases. Calder6n-Zygmund operator, discrete Calder6n formula, Hardy space, Plancherel-Plrya inequality, Littlewood-Paley g function, Tb theorem Acknowledgements and Notes. This article was written while the first author was visiting the National Center for Theoretical Sciences in Taiwan. He would like to thank the National Center for Theoretical Sciences for its warm hospitality and support of this research. Research by the third author was supported in part by the National Science Council.",
year = "2004",
doi = "10.1007/BF02922074",
language = "???core.languages.en_GB???",
volume = "14",
pages = "291--318",
journal = "Journal of Geometric Analysis",
issn = "1050-6926",
number = "2",
}