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Hardy–Littlewood–Sobolev Inequality on Mixed-Norm Lebesgue Spaces

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Abstract

We study the Hardy–Littlewood–Sobolev inequality on mixed-norm Lebesgue spaces. We give a complete characterization of indices \(\vec p\) and \(\vec q\) such that the Riesz potential is bounded from \(L^{\vec p}\) to \(L^{\vec q}\). In particular, all the endpoint cases are studied. As a result, we get the mixed-norm Hardy–Littlewood–Sobolev inequality.

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Acknowledgements

The authors thank the referees very much for valuable suggestions which helped to improve the paper.

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  1. School of Mathematical Sciences and LPMC, Nankai University, Tianjin, 300071, China

    Ting Chen & Wenchang Sun

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  1. Ting Chen
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Correspondence to Wenchang Sun.

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This work was partially supported by the National Natural Science Foundation of China (11801282, U21A20426 and 12171250).

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Chen, T., Sun, W. Hardy–Littlewood–Sobolev Inequality on Mixed-Norm Lebesgue Spaces. J Geom Anal 32, 101 (2022). https://doi.org/10.1007/s12220-021-00855-2

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