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arXiv · 1912.03712

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

Ting Chen·Wenchang Sun
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Abstract

We consider 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 $L^{\vec q}$, including all the endpoint cases. As a result, we get the mixed-norm Hardy-Littlewood-Sobolev inequality.

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Ting Chen, Wenchang Sun. 2019-12-08. Hardy-Littlewood-Sobolev Inequality on Mixed-Norm Lebesgue Spaces. https://arxiv.org/abs/1912.03712

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