Boundedness of Calderón-Zygmund operators on weighted product hardy spaces

研究成果: 雜誌貢獻期刊論文同行評審

2 引文 斯高帕斯(Scopus)

摘要

Let T be a singular integral operator in Journé's class with regularity exponent ε, w ∈ Aq, 1 ≤ q < 1 + ε, and q/(1 + ε) < p ≤ 1. We obtain the Hpw(R×R)-Lpw (R2) boundedness of T by using R. Fefferman's "trivial lemma" and Journé's covering lemma. Also, using the vector-valued version of the "trivial lemma" and Littlewood-Paley theory, we prove the Hpw (R×R)-boundedness of T provided T*1(1) = T*2(1) = 0; that is, the reduced T1 theorem on Hpw(R×R). In order to show these two results, we demonstrate a new atomic decomposition of Hpw(R×R) ∩ L2w(R2), for which the series converges in L2w. Moreover, a fundamental principle that the boundedness of operators on the weighted product Hardy space can be obtained simply by the actions of such operators on all atoms is given.

原文???core.languages.en_GB???
頁(從 - 到)115-133
頁數19
期刊Journal of Operator Theory
72
發行號1
DOIs
出版狀態已出版 - 2014

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