Some Inequalities for the Fourier Transform and Their Limiting Behaviour-Reference-Cited by-同舟云学术

Some Inequalities for the Fourier Transform and Their Limiting Behaviour

Published:2023-12-29 Issue:2 Volume:34 Page:
ISSN:1050-6926
Container-title:The Journal of Geometric Analysis
language:en
Short-container-title:J Geom Anal

Author:

Garofalo Nicola

Abstract

AbstractWe identify a one-parameter family of inequalities for the Fourier transform whose limiting case is the restriction conjecture for the sphere. Using Stein’s method of complex interpolation, we prove the conjectured inequalities when the target space is

$$L^2$$

L 2 , and show that this recovers in the limit the celebrated Tomas-Stein theorem.

Funder

Università degli Studi di Padova

Publisher

Springer Science and Business Media LLC

Subject

Geometry and Topology

Link

https://link.springer.com/content/pdf/10.1007/s12220-023-01477-6.pdf

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