A Note on $H^p_w$-Boundedness of Riesz Transforms and $\theta$-Calderόn-Zygmund Operators Through Molecular Characterization
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
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Muckenhoupt weight Riesz transform Calderón-Zygmund operator.
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