Bilinear spherical maximal function with fractal dilations
Surjeet Singh Choudhary, Chun-Yen Shen, Saurabh Shrivastava
公開日: 2025/10/3
Abstract
In this paper, we investigate $L^p-$boundedness of the bilinear spherical maximal function associated with a general dilation set $E\subset\R_+$. 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 $p_1=1$ or $p_2=1$ in dimension $d\geq4$.