A Note on $H^p_w$-Boundedness of Riesz Transforms and $\theta$-Calderόn-Zygmund Operators Through Molecular Characterization

doi:10.1007/s10496-011-0251-z

A Note on $H^p_w$ -Boundedness of Riesz Transforms and $\theta$ -Calderόn-Zygmund Operators Through Molecular Characterization

$A Note on $H^p_w$-Boundedness of Riesz Transforms and $\theta$-Calderόn-Zygmund Operators Through Molecular Characterization$

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Year: 2011

Analysis in Theory and Applications, Vol. 27 (2011), Iss. 3 : pp. 251–264

Abstract

Let $0 <p \leq 1$ and $w$ in the Muckenhoupt class $A_1$ . Recently, by using the weighted atomic decomposition and molecular characterization, Lee, Lin and Yang^[11] established that the Riesz transforms $R_j$ , $j = 1,2, \cdots ,n$ , are bounded on $H^p_w(\mathbf{R}^n)$ . In this note we extend this to the general case of weight $w$ in the Muckenhoupt class $A_\infty$ through molecular characterization. One difficulty, which has not been taken care in [11], consists in passing from atoms to all functions in $H^p_w(\mathbf{R}^n)$ . Furthermore, the $H^p_w$ -boundedness of $\theta$ -Calderón-Zygmund operators are also given through molecular characterization and atomic decomposition.

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Journal Article Details

Publisher Name: Global Science Press

Language: English

DOI: https://doi.org/10.1007/s10496-011-0251-z

Analysis in Theory and Applications, Vol. 27 (2011), Iss. 3 : pp. 251–264

Published online: 2011-01

AMS Subject Headings: Global Science Press

Pages: 14

Keywords: Muckenhoupt weight Riesz transform Calderón-Zygmund operator.

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