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arXiv · 1803.02581

Regularity of fractional maximal functions through Fourier multipliers

David Beltran·João Pedro Ramos·Olli Saari
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Abstract

We prove endpoint bounds for derivatives of fractional maximal functions with either smooth convolution kernel or lacunary set of radii in dimensions $n \geq 2$. We also show that the spherical fractional maximal function maps $L^{p}$ into a first order Sobolev space in dimensions $n \geq 5$.

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David Beltran, João Pedro Ramos, Olli Saari. 2018-03-07. Regularity of fractional maximal functions through Fourier multipliers. https://doi.org/10.1016/j.jfa.2018.11.004

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