Improved bounds for Stein's square functions

Details Improved bounds for Stein's square functions Improved bounds for Stein's square functions

2010-12-10

arxiv.org/abs/1012.2159v2

Mathematics

Classical Analysis and ODEs

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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