A Pólya–Szegö principle for general fractional Orlicz–Sobolev spaces

Abstract

In this article, we prove modular and norm Pólya–Szegö inequalities in general fractional Orlicz–Sobolev spaces by using the polarization technique. We introduce a general framework which includes the different definitions of these spaces in the literature, and we establish some of its basic properties such as the density of smooth functions. As a corollary, we prove a Rayleigh–Faber–Krahn type inequality for Dirichlet eigenvalues under nonlocal nonstandard growth operators.