New bounds for Stein's square function in ${\mathbb{R}}^3$

Abstract

We prove new $L^p({\mathbb{R}}^3)$ bounds on Stein's square function for $p\ge 3.25$. As an application, it improves the maximal Bochner-Riesz conjecture to the same range of $p$.

arXiv comment54 pages

References in corpus (2)

• A restriction estimate in ${\mathbb{R}}^3$ using brooms
• On the Bochner-Riesz operator in ${\mathbb{R}}^3$

Cited by in corpus (1)

• New bounds for Stein's square functions in higher dimensions