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Interpolations of Mixed-Norm Function Spaces

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Abstract

This article is devoted to presenting a general interpolation result on mixed-norm function spaces generated by quasi-Banach lattices. Under certain conditions, the authors show that such mixed-norm function spaces are closed under the Calderón product and the ± interpolation method. As applications, the authors obtain some new interpolation results for mixed-norm variable Lebesgue spaces, mixed-norm Lorentz spaces, and mixed-norm Morrey spaces.

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Acknowledgements

The authors would like to thank the referees for their carefully reading and helpful comments which indeed improve the presentation of this article.

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Authors and Affiliations

  1. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, People’s Republic of China

    Suqing Wu

  2. Laboratory of Mathematics and Complex Systems (Ministry of Education of China), School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, People’s Republic of China

    Dachun Yang & Wen Yuan

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  1. Suqing Wu
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  2. Dachun Yang
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  3. Wen Yuan
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Correspondence to Wen Yuan.

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Communicated by Rosihan M. Ali.

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This project is supported by the National Natural Science Foundation of China (Grant Nos. 11971058, 12071197 and 11871100) and the National Key Research and Development Program of China (Grant No. 2020YFA0712900)

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Wu, S., Yang, D. & Yuan, W. Interpolations of Mixed-Norm Function Spaces. Bull. Malays. Math. Sci. Soc. 45, 153–175 (2022). https://doi.org/10.1007/s40840-021-01187-8

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