TY - JOUR
T1 - Isoperimetric inequalities for Schatten norms of Riesz potentials
AU - Rozenblum, G.
AU - Ruzhansky, M.
AU - Suragan, D.
N1 - Publisher Copyright:
© 2016 The Authors.
PY - 2016/7/1
Y1 - 2016/7/1
N2 - 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.
AB - 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.
KW - Hong-Krahn-Szegö inequality
KW - Rayleigh-Faber-Krahn inequality
KW - Riesz potential
KW - Schatten p-norm
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U2 - 10.1016/j.jfa.2016.04.023
DO - 10.1016/j.jfa.2016.04.023
M3 - Article
AN - SCOPUS:84964647549
SN - 0022-1236
VL - 271
SP - 224
EP - 239
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 1
ER -