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The Journal of Geometric Analysis

, Volume 29, Issue 2, pp 1259–1301 | Cite as

A Constrained Optimization Problem for the Fourier Transform: Quantitative Analysis

  • Dominique MaldagueEmail author
Article
  • 44 Downloads

Abstract

Among functions f majorized by indicator functions \(1_E\), which functions have maximal ratio \(\Vert {\widehat{f}}\Vert _q/|E|^{1/p}\)? We establish a quantitative answer to this question for exponents q sufficiently close to even integers, building on previous work proving the existence of such maximizers.

Keywords

Harmonic analysis Extremization Fourier transform Quantitative analysis 

Mathematics Subject Classification

42A16 42B10 

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Copyright information

© Mathematica Josephina, Inc. 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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