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arXiv · 2310.17885

Sobolev regularity for a class of local fractional new maximal operators

Rui Li·Shuangping Tao
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Abstract

This paper is devoted to studying the regularity properties for the new maximal operator $M_{\varphi}$ and the fractional new maximal operator $M_{\varphi,\beta}$ in the local case. Some new pointwise gradient estimates of $M_{\varphi,\Omega}$ and $M_{\varphi,\beta,\Omega}$ are given. Moreover, the boundedness of $M_{\varphi,\Omega}$ and $M_{\varphi,\beta,\Omega}$ on Sobolev space is established. As applications, we also obtain the bounds of the above operators on Sobolev space with zero boundary values.

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BibTeXRIS

Rui Li, Shuangping Tao. 2023-10-27. Sobolev regularity for a class of local fractional new maximal operators. https://arxiv.org/abs/2310.17885

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