Survey on bilinear spherical averages and associated maximal operators

2025/02/04 by Tainara Borges, Borges, Tainara
Mathematics · #Advanced Harmonic Analysis Research #Mathematical Approximation and Integration #Approximation Theory and Sequence Spaces

paper · pdf · doi:10.48550/arxiv.2502.02765

Abstract

In this survey, we collect recent progress in the understanding of L^p bounds for bilinear spherical averages and some associated maximal functions like the bilinear spherical maximal function and its lacunary counterpart. We describe necessary conditions satisfied by triples in the L^p improving region of a bilinear spherical averaging operator and the localized bilinear spherical maximal function, as well as describe the best-known boundedness regions to date. We state some open questions along the way to motivate future research on this topic, and we exploit some possible generalizations.

Related

• L^p-estimates for uncentered spherical averages and lacunary maximal functions
• Sparse bounds for the bilinear spherical maximal function
• Maximal estimates for the bilinear spherical averages and the bilinear Bochner-Riesz operators
• Bounds for lacunary bilinear spherical and triangle maximal functions
• L^p improving properties and maximal estimates for certain multilinear averaging operators