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Hausdorff Operator on Morrey Spaces and Campanato Spaces

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Abstract

We study the high-dimensional Hausdorff operators on the Morrey space and on the Campanato space. We establish their sharp boundedness on these spaces. Particularly, our results solve an open question posted by E. Liflyand (2013).

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Acknowledgments

The first author would like to express his deep thanks to Professor Silei Wang for his private communication and help. The authors cordially thank the anonymous referees for their valuable comments which led to the improvement of this paper.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang International Studies University, 299 Liuhe Road, Xihu, Hangzhou, 310014, P. R. China

    Jianmiao Ruan & Hongliang Li

  2. Department of Mathematical Sciences, University of Wisconsin-Milwaukee, PO Box 413, Milwaukee, WI, 53201-0413, USA

    Dashan Fan

Authors
  1. Jianmiao Ruan
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  2. Dashan Fan
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  3. Hongliang Li
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Corresponding author

Correspondence to Jianmiao Ruan.

Additional information

The research was supported by the Zhejiang Provincial Natural Science Foundation of China (No. LY18A010015), the National Natural Science Foundation of China (Nos. 11771358, 11871436) and the “BoDa” Research Program of Zhejiang International Studies University (No. BD2019B5).

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Ruan, J., Fan, D. & Li, H. Hausdorff Operator on Morrey Spaces and Campanato Spaces. Czech Math J 70, 505–517 (2020). https://doi.org/10.21136/CMJ.2019.0386-18

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  • DOI: https://doi.org/10.21136/CMJ.2019.0386-18

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