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Lipschitz-Type Characterizations of Musielak–Orlicz-Campanato Spaces

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Abstract

In this paper, the authors establish a Lipschitz-type characteriztion for Musielak–Orlicz-Campanato spaces. As applications, since pointwise multipliers on Orlicz-Campanato spaces provide natural examples of Musielak–Orlicz-Campanato functions, the authors obtain Lipschitz-type characterizations for both Orlicz-Campanato spaces and their pointwise multiplier spaces. Typical examples of such Orlicz-Campanato spaces include not only classical Campanato spaces but also Campanato spaces with an extra logarithmic smoothness.

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Acknowledgements

The authors are very grateful to Professor Aline Bonami for providing us some details on the proof of Proposition 6.5 and, especially, the idea of considering a rotated cone that was away from the first coordinate. The authors would like to thank Professors Dachun Yang and Wen Yuan for their helpful discussions on the topic of this article. The authors are also grateful to the anonymous referee for careful reading and valuable comments that helped to improve this article.

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  1. School of Mathematics, Renmin University of China, Bei**g, 100872, People’s Republic of China

    Chenglong Fang & Liguang Liu

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  1. Chenglong Fang
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  2. Liguang Liu
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Correspondence to Liguang Liu.

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LL was supported by the National Natural Science Foundation of China (# 12371102).

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Fang, C., Liu, L. Lipschitz-Type Characterizations of Musielak–Orlicz-Campanato Spaces. J Geom Anal 33, 380 (2023). https://doi.org/10.1007/s12220-023-01449-w

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