Geometric maximizers of Schatten norms of some convolution type integral operators

Abstract

In this paper we prove that the ball is a maximizer of the Schatten $p$-norm of some convolution type integral operators with non-increasing kernels among all domains of a given measure in ${\mathbb{R}}^d$. We also show that the equilateral triangle has the largest Schatten $p$-norm among all triangles of a given area. Some physical motivations for our results are also presented.

to appear in JMAA. arXiv admin note: text overlap with arXiv:1503.08390

References in corpus (2)

• Schatten classes on compact manifolds: Kernel conditions
• Kernel and symbol criteria for Schatten classes and $r$-nuclearity on compact manifolds