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Isoperimetric inequalities for Schatten norms of Riesz potentials. / Rozenblum, G.; Ruzhansky, M.; Suragan, D.

In: Journal of Functional Analysis, Vol. 271, No. 1, 01.07.2016, p. 224-239.

Research output: Contribution to journal › Article › peer-review

Harvard

Rozenblum, G, Ruzhansky, M & Suragan, D 2016, 'Isoperimetric inequalities for Schatten norms of Riesz potentials', Journal of Functional Analysis, vol. 271, no. 1, pp. 224-239. https://doi.org/10.1016/j.jfa.2016.04.023

APA

Rozenblum, G., Ruzhansky, M., & Suragan, D. (2016). Isoperimetric inequalities for Schatten norms of Riesz potentials. Journal of Functional Analysis, 271(1), 224-239. https://doi.org/10.1016/j.jfa.2016.04.023

Vancouver

Rozenblum G, Ruzhansky M, Suragan D. Isoperimetric inequalities for Schatten norms of Riesz potentials. Journal of Functional Analysis. 2016 Jul 1;271(1):224-239. https://doi.org/10.1016/j.jfa.2016.04.023

Author

Rozenblum, G. ; Ruzhansky, M. ; Suragan, D. / Isoperimetric inequalities for Schatten norms of Riesz potentials. In: Journal of Functional Analysis. 2016 ; Vol. 271, No. 1. pp. 224-239.

BibTeX

@article{a447d3bcbbc2460ebe81598e6cd568e6,
title = "Isoperimetric inequalities for Schatten norms of Riesz potentials",
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 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-Szeg{\"o} inequalities.",
keywords = "Hong-Krahn-Szeg{\"o} inequality, Rayleigh-Faber-Krahn inequality, Riesz potential, Schatten p-norm",
author = "G. Rozenblum and M. Ruzhansky and D. Suragan",
year = "2016",
month = jul,
day = "1",
doi = "10.1016/j.jfa.2016.04.023",
language = "English",
volume = "271",
pages = "224--239",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
publisher = "Elsevier",
number = "1",

}

RIS

TY - JOUR

T1 - Isoperimetric inequalities for Schatten norms of Riesz potentials

AU - Rozenblum, G.

AU - Ruzhansky, M.

AU - Suragan, D.

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

UR - http://www.scopus.com/inward/record.url?scp=84964647549&partnerID=8YFLogxK

U2 - 10.1016/j.jfa.2016.04.023

DO - 10.1016/j.jfa.2016.04.023

M3 - Article

AN - SCOPUS:84964647549

VL - 271

SP - 224

EP - 239

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 1

ER -

ID: 50650350