New bounds for Stein's square functions in higher dimensions

Abstract

We improve the $L^p({\mathbb{R}}^n)$ bounds on Stein's square function to the best-known range of the Fourier restriction problem when $n\ge 4$. Applications including certain local smoothing estimates are also discussed.

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References in corpus (1)

• On the Bochner-Riesz operator in ${\mathbb{R}}^3$