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 Rd. 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-Szegö inequalities.

Original languageEnglish
Pages (from-to)224-239
Number of pages16
JournalJournal of Functional Analysis
Volume271
Issue number1
DOIs
StatePublished - 1 Jul 2016

    Scopus subject areas

  • Analysis

    Research areas

  • Hong-Krahn-Szegö inequality, Rayleigh-Faber-Krahn inequality, Riesz potential, Schatten p-norm

ID: 50650350