Existence of extremals for a Fourier restriction inequality
- 27 August 2012
- journal article
- Published by Mathematical Sciences Publishers in Analysis & PDE
- Vol. 5 (2), 261-312
- https://doi.org/10.2140/apde.2012.5.261
Abstract
The adjoint Fourier restriction inequality of Tomas and Stein states that the mapping $f\mapsto \widehat{f\sigma}$ is bounded from $\lt(S^2)$ to $L^4(\reals^3)$. We prove that there exist functions which extremize this inequality, and that any extremizing sequence of nonnegative functions has a subsequence which converges to an extremizer.
Keywords
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