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.
Acknowledgments
All of the authors are members of CONICET.
Disclosure statement
No potential conflict of interest was reported by the author(s).