Regularity of fractional maximal functions through Fourier multipliers

Abstract

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

arXiv commentfinal version, to appear in Journal of Functional Analysis

References in corpus (7)

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Cited by in corpus (6)

• Gradient bounds for radial maximal functions
• Weak differentiability for fractional maximal functions of general $L^p$ functions on domains
• Regularity of maximal operators: recent progress and some open problems
• $L^p-L^q$ local smoothing estimates for the wave equation via $k$-broad Fourier restriction
• Sobolev contractivity of gradient flow maximal functions
• The Variation of the Uncentered Maximal Operator with respect to Cubes