Improved bounds for Stein's square functions

Published 10 Dec 2010 in math.CA and math.AP | (1012.2159v2)

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 Schr\"odinger equations.

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