Bilinear spherical maximal function with fractal dilations

2025/10/03 by Choudhary, Surjeet Singh, Shen, Chun-Yen, Shrivastava, Saurabh
#42B15 #42B25 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.03094

Abstract

In this paper, we investigate L^p-boundedness of the bilinear spherical maximal function associated with a general dilation set E⊂\R₊. We quantify the range of L^p-boundedness in terms of a dilation-invariant notion of upper Minkowski dimension of the set E. A particular case of this study settles an open question of L^p-boundedness of the lacunary bilinear spherical maximal function at borderline cases p₁=1 or p₂=1 in dimension d≥4.

Citations

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• Bilinear Spherical Maximal Function
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• Lacunary spherical means

Related

• Bilinear Spherical Maximal Function
• Problems on spherical maximal functions
• Spherical maximal operators with fractal sets of dilations on radial functions
• Sharp endpoint L^p-estimates for Bilinear spherical maximal functions
• Multilinear Spherical Maximal Function