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A comparison principle for convolution measures with applications

Part of: Harmonic analysis in several variables Harmonic analysis in one variable Functions of several variables

Published online by Cambridge University Press:  28 June 2019

DIOGO OLIVEIRA E SILVA  and
RENÉ QUILODRÁN
DIOGO OLIVEIRA E SILVA
Affiliation:
School of Mathematics, University of Birmingham, Edgbaston, Birmingham, B15 2TT. e-mail: [email protected]
RENÉ QUILODRÁN
Affiliation:
e-mail: [email protected]
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Abstract

We establish the general form of a geometric comparison principle for n-fold convolutions of certain singular measures in ℝd which holds for arbitrary n and d. This translates into a pointwise inequality between the convolutions of projection measure on the paraboloid and a perturbation thereof, and we use it to establish a new sharp Fourier extension inequality on a general convex perturbation of a parabola. Further applications of the comparison principle to sharp Fourier restriction theory are discussed in the companion paper [3].

MSC classification

Primary: 42A85: Convolution, factorization
Secondary: 42B10: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type 26B10: Implicit function theorems, Jacobians, transformations with several variables
Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 169 , Issue 2 , September 2020 , pp. 307 - 322
Copyright
© Cambridge Philosophical Society 2019

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