On the limit as $s\to 0^+$ of fractional Orlicz-Sobolev spaces

Angela Alberico; Andrea Cianchi; Luboš Pick; Lenka Slavíková

paper

On the limit as $s \to 0^{+}$ of fractional Orlicz-Sobolev spaces

arXiv:2002.05449

Abstract

An extended version of the Maz'ya-Shaposhnikova theorem on the limit as $s \to 0^{+}$ of the Gagliardo-Slobodeckij fractional seminorm is established in the Orlicz space setting. Our result holds in fractional Orlicz-Sobolev spaces associated with Young functions satisfying the $Δ_{2}$ -condition, and, as shown by counterexamples, it may fail if this condition is dropped.

On the limit as s→0+ of fractional Orlicz-Sobolev spaces

Abstract

On the limit as $s \to 0^{+}$ of fractional Orlicz-Sobolev spaces