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Isoperimetric inequalities for Schatten norms of Riesz potentials

Journal article
Authors Grigori Rozenblioum
M. Ruzhansky
D. Suragan
Published in Journal of Functional Analysis
Volume 271
Issue 1
Pages 224-239
ISSN 0022-1236
Publication year 2016
Published at Department of Mathematical Sciences, Mathematics
Pages 224-239
Language en
Links dx.doi.org/10.1016/j.jfa.2016.04.02...
https://gup.ub.gu.se/file/193304
Keywords Riesz potential, Schatten p-norm, Rayleigh-Faber-Krahn inequality, Hong-Krahn-Szego inequality
Subject categories Mathematics

Abstract

In this note we prove that the ball is a maximiser for integer order Schatten p-norms of the Riesz potential operators among all domains of a given measure in R-d. In particular, the result is valid for the polyharmonic Newton potential operator, which is related to a nonlocal boundary value problem for the poly-Laplacian extending the one considered by M. Kac in the case of the Laplacian, so we obtain isoperimetric inequalities for its eigenvalues as well, namely, analogues of Rayleigh-Faber-Krahn. and Hong-Krahn-Szego inequalities.

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