Radial Fourier multipliers in high dimensions

Details Radial Fourier multipliers in high dimensions Radial Fourier multipliers in high dimensions

2009-02-05

arxiv.org/abs/0902.0943v2

Acta Mathematica, 206, No 1 (2011), 55-92

Mathematics

Classical Analysis and ODEs

Some changes in the last section

Scientific paper

Given a fixed $p\neq 2$, we prove a simple and effective characterization of
all radial multipliers of $\cF L^p(\Bbb R^d)$, provided that the dimension $d$
is sufficiently large. The method also yields new $L^q$ space-time regularity
results for solutions of the wave equation in high dimensions.

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