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A Hardy–Littlewood Type Theorem for Harmonic Bergman–Orlicz Spaces and Applications

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Abstract

It is well known that a harmonic function is in a Bergman space if and only if it satisfies some Hardy–Littlewood type integral estimates. In this paper, we extend this result to harmonic Bergman–Orlicz spaces. As an application, Lipschitz-type characterizes of harmonic Bergman–Orlicz spaces on the unit ball with respect to pseudo-hyperbolic, hyperbolic and Euclidean metrics are established. In addition, the boundedness of a mapping defined by a difference quotient of harmonic function is discussed.

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ACKNOWLEDGMENTS

The research of this paper was finished when the first author was an academic visitor in Shanghai Jiaotong University. He thanks Professor Miaomiao Zhu for the invitation and many useful suggestions. In particular, the authors express their hearty thanks to the referee for his/her careful reading of this paper and many useful suggestions.

Funding

The research was partly supported by the Natural Science Foundation of Fujian Province (no. 2020J05157), the Research projects of Young and Middle-Aged Teacher’s Education of Fujian Province (no. JAT190508).

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Authors and Affiliations

  1. School of Mathematics, Physics and Statistics, Shanghai Polytechnic University, Shanghai, China

    Xi Fu

  2. School of Mathematics, Quanzhou Normal University, Fujian, P. R. China

    Q. Shi#

Authors
  1. Xi Fu
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  2. Q. Shi#
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Correspondence to Xi Fu or Q. Shi#.

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The authors declare that they have no conflicts of interest.

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Fu, X., Shi#, Q. A Hardy–Littlewood Type Theorem for Harmonic Bergman–Orlicz Spaces and Applications. J. Contemp. Mathemat. Anal. 58, 303–314 (2023). https://doi.org/10.3103/S1068362323050096

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  • DOI: https://doi.org/10.3103/S1068362323050096

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