Improved bounds for Stein's square functions

Mathematics – Classical Analysis and ODEs

Scientific paper

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Scientific paper

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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