A note on isoperimetric inequalities for logarithmic potentials

We give an inequality for all Schatten p  -norms with p≥2p≥2, on a class of bounded domains majorized by a given domain. We partially prove the Ruzhansky–Suragan's conjecture [12], by showing that for any integer p≥3p≥3, the square (cube) is a maximizer of Schatten p-norm of the logarithmic (Newtonian) potential among all rectangles (rectangular parallelepipeds) of a given Lebesgue measure.