Sparse bounds for the bilinear spherical maximal function

Tainara Borges, Benjamin R. Foster, Yumeng Ou, Jill Pipher, Zirui Zhou

Type: Article

Publication Date: 2023-01-18

Citations: 6

DOI: https://doi.org/10.1112/jlms.12715

Abstract

Abstract We derive sparse bounds for the bilinear spherical maximal function in any dimension . When , this immediately recovers the sharp bound of the operator and implies quantitative weighted norm inequalities with respect to bilinear Muckenhoupt weights, which seems to be the first of their kind for the operator. The key innovation is a group of newly developed continuity improving estimates for the single‐scale bilinear spherical averaging operator.

Locations

Journal of the London Mathematical Society - View - PDF
arXiv (Cornell University) - View - PDF

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+ PDF Chat	Restriction of Fourier transforms to curves and related oscillatory integrals	2009	Jong-Guk Bak Daniel M. Oberlin Andreas Seeger
+ PDF Chat	Multilinear convolutions defined by measures on spheres	1988	Daniel M. Oberlin
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+	Maximal functions: Spherical means	1976	Elias M. Stein
+	Endpoint Inequalities for Spherical Multilinear Convolutions	1998	Jong-Guk Bak Yongsun Shim
+ PDF Chat	On triangles determined by subsets of the Euclidean plane, the associated bilinear operators and applications to discrete geometry	2012	Allan Greenleaf Alex Iosevich
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