Improved bounds for Stein's square functions

Abstract

We prove a weighted norm inequality for the maximal Bochner--Riesz operator and the associated square-function. This yields new $L^p(R^d)$ bounds on classes of radial Fourier multipliers for $p\ge 2+4/d$ with $d\ge 2$, as well as space-time regularity results for the wave and Schrödinger equations.

Cited by in corpus (8)

• Sharp resolvent estimates outside of the uniform boundedness range
• Square function estimates for the Bochner-Riesz means
• On radial Fourier multipliers and almost everywhere convergence
• Sharp variation-norm estimates for oscillatory integrals related to Carleson's theorem
• Multi-scale sparse domination
• Subdyadic square functions and applications to weighted harmonic analysis
• Optimal control of singular Fourier multipliers by maximal operators
• Discrete analogues of maximally modulated singular integrals of Stein-Wainger type: ${\ell }^p$ bounds for $p>1$