Xinyu Gao

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20242026

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math.CA2026

A.E. Convergence vs Boundedness

Xinyu Gao, Loukas Grafakos

We extend Stein's maximal theorem to the bilinear setting. Let $M$ be a homogeneous space with a transitive action of a compact abelian group, and let $1 \leq p, q \leq 2$ and $1/2 \l…

math.CA2024

Lebesgue bounds for multilinear spherical and lacunary maximal averages

Xinyu Gao

We establish $L^{p_{1}} (R^{d}) \times \dots \times L^{p_{n}} (R^{d}) \to L^{r} (R^{d})$ bounds for spherical averaging operators $A^{n}$ in dimensions $d…