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- Title
Hardy spaces and the Tb theorem.
- Authors
Han, Yongsheng; Lee, Ming-Yi; Lin, Chin-Cheng
- Abstract
It is well-known that Calderón-Zygmund operators T are bounded on Hp for $$\frac{n}{{n + 1}}< p \leqslant 1$$ 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 Hp to a new Hardy space H. To develop an H theory, a discrete Calderón-type reproducing formula and Plancherel-Pôlya-type inequalities associated to a para-accretive function are established. Moreover, David, Journé, and Semmes’ result [9] about the LP, 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 Calderón-Zygmund operator theory.
- Publication
Journal of Geometric Analysis, 2004, Vol 14, Issue 2, p291
- ISSN
1050-6926
- Publication type
Article
- DOI
10.1007/BF02922074