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Boundedness of Singular Integral Operators on Local Hardy Spaces and Dual Spaces

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Abstract

The purpose of this paper is to provide necessary and sufficient conditions of the boundedness for singular integrals on the local Hardy space and its dual. Particularly the singular integrals considered in this paper include the pseudo-differential operators

$T_{\sigma }f(x)=\int \limits \sigma (x \xi )e^{2\pi ix\xi }\hat {f}(\xi )d\xi $

with \(\sigma \in S_{1 0}^{0}\). As a consequence our results give another proof of the boundedness of the pseudo-differential operators on the local Hardy space (Goldberg Duke Math. J. 46(1) 27–42 1979).

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Acknowledgements

The authors would like to thank the referee for his∖her very helpful comments and suggestions which have improved the exposition of the paper.

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Authors and Affiliations

  1. School of Sciences, Nantong University, Nantong, 226007, People’s Republic of China

    Wei Ding

  2. Department of Mathematics, Auburn University, Auburn, AL, 226010, USA

    YongSheng Han

  3. Department of Mathematics, Nantong Normal College, Nantong, 226010, People’s Republic of China

    YuePing Zhu

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  1. Wei Ding
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  2. YongSheng Han
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Correspondence to Wei Ding.

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Supported by NNSF of China grants (11501308 11771223).

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Ding, W., Han, Y. & Zhu, Y. Boundedness of Singular Integral Operators on Local Hardy Spaces and Dual Spaces. Potential Anal 55, 419–441 (2021). https://doi.org/10.1007/s11118-020-09863-3

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