Hausdorff Operator on Morrey Spaces and Campanato Spaces

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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Correspondence to Jianmiao Ruan.

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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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Keywords

  • Hausdorff operator
  • Morrey space
  • Campanato space

MSC 2010

  • 42B35
  • 42B30
  • 46E30