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arXiv · 2404.00430

Variational inequalities for generalized spherical means

Wenjuan Li·Dongyong Yang·Feng Zhang
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Abstract

In this paper, we establish the $L^{p}(\mathbb{R}^{d})$-boundedness of the variation operator and the $\delta$-jump operator for generalized spherical means, and we also show the necessary conditions for the $L^{p}(\mathbb{R}^{d})$-boundedness of these operators. These results are almost optimal when $d=2$.

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Wenjuan Li, Dongyong Yang, Feng Zhang. 2024-03-30. Variational inequalities for generalized spherical means. https://arxiv.org/abs/2404.00430

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