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

SALORT, ARIEL; SALORT, ARIEL; DE NÁPOLI, PABLO; DE NÁPOLI, PABLO; FERNÁNDEZ BONDER, JULIÁN; FERNÁNDEZ BONDER, JULIÁN

Complex Variables and Elliptic Equations

Taylor and Francis Ltd.

Año: 2020 vol. 2020 p. 1 - 23

1747-6933

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.