An isoperimetric inequality for an integral operator on flat tori (Q327413)

The authors consider an integral operator NEWLINE\[NEWLINE A_f\psi(x)=\int_{T} f(d^2(x,y))\psi(y)dy NEWLINE\]NEWLINE on a flat torus \(T\) with \(d\) denoting the distance function and \(f\) positive and non-increasing. They show that for a fixed \(f\), the equilateral torus maximizes both the \(L^2\) operator norm and the Hilbert-Schmidt norm of \(A_f\). The proof uses rearrangement methods. An appendix contains a translation of the proof of the Fejes Tóth Moment Lemma.