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arXiv · 2502.02765

Survey on bilinear spherical averages and associated maximal operators

Tainara Borges
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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.

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Tainara Borges. 2026-03-02. Survey on bilinear spherical averages and associated maximal operators. https://arxiv.org/abs/2502.02765

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