A type theorem on the weighted Herz‐type Hardy spaces and applications |
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| Authors: | Jianmiao Ruan Lijing Sun Huoxiong Wu Xiao Yu |
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| Institution: | 1. Department of Mathematics, Zhejiang International Studies University, Hangzhou, China;2. Department of Mathematical Sciences, University of Wisconsin‐Milwaukee, Milwaukee, WI, USA;3. School of Mathematical Sciences, Xiamen University, Xiamen, China;4. Department of Mathematics, Shangrao Normal University, Shangrao, China |
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| Abstract: | This paper gives a  type theorem, which is a boundedness criterion for singular integral operators from the weighted Herz‐type Hardy spaces into the weighted local Herz‐type Hardy spaces. As applications, the corresponding mapping properties for the Cauchy integral and Calderón's commutators are obtained. In addition, a counter example is shown that neither is a Calderón–Zygmund singular integral operator bounded on the homogeneous local Herz‐type Hardy space, nor bounded on the classical local Hardy space. |
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| Keywords: | Singular integral the Cauchy integral the Calderó n commutator weighted Herz‐type Hardy spaces 42B20 42B35 42B99 |
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