Discrete Riesz Potentials on Discrete Weighted Morrey Spaces

Xuebing Hao; Shuai Yang; Baode Li

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arXiv · 2310.08458

Discrete Riesz Potentials on Discrete Weighted Morrey Spaces

Xuebing Hao·Shuai Yang·Baode Li

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Abstract

Let $0<\alpha<1$. We obtain the boundedness of the discrete fractional Hardy-Littlewood maximal operators ${\mathcal M}_\alpha$ on discrete weighted Lebesgue spaces. From this and a discrete version of Whitney decomposition theorem, we deduce the boundedness of the discrete Riesz potentials $I_\alpha$ on discrete weighted Lebesgue spaces. The boundedness of $I_\alpha$ on discrete weighted Morrey spaces is further obtained. Moreover, the boundedness of ${\mathcal M}_\alpha$ is also obtained which is new even for unweighted case.

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BibTeX RIS

Xuebing Hao, Shuai Yang, Baode Li. 2023-10-12. Discrete Riesz Potentials on Discrete Weighted Morrey Spaces. https://arxiv.org/abs/2310.08458

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