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# Atomic Decomposition and Boundedness of Operators on Weighted Hardy Spaces

Published:2011-04-15
Printed: Jun 2012
• Yongsheng Han,
Department of Mathematics, Auburn University, Auburn, AL 36849-5310, U.S.A.
• Ming-Yi Lee,
Department of Mathematics, National Central University, Chung-Li, Taiwan 320, Republic of China
• Chin-Cheng Lin,
Department of Mathematics, National Central University, Chung-Li, Taiwan 320, Republic of China
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## Abstract

In this article, we establish a new atomic decomposition for $f\in L^2_w\cap H^p_w$, where the decomposition converges in $L^2_w$-norm rather than in the distribution sense. As applications of this decomposition, assuming that $T$ is a linear operator bounded on $L^2_w$ and $0  Keywords:$A_p$weights, atomic decomposition, Calderón reproducing formula, weighted Hardy spaces  MSC Classifications: 42B25 - Maximal functions, Littlewood-Paley theory 42B30 -$H^p\$-spaces