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Atomic Decomposition and Boundedness of Operators on Weighted Hardy Spaces
  Published:2011-04-15
 Printed: Jun 2012
Canadian Mathematical Bulletin
  • 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 $A_p$ weights, atomic decomposition, Calderón reproducing formula, weighted Hardy spaces
MSC Classifications: 42B25, 42B30 show english descriptions Maximal functions, Littlewood-Paley theory
$H^p$-spaces 42B25 - Maximal functions, Littlewood-Paley theory
42B30 - $H^p$-spaces
 
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