An extended version of the Maz'ya-Shaposhnikova theorem on the limit as s -> 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 \Delta2-condition, and, as shown by counterexamples, it may fail if this condition is dropped.
On the limit as $s\to 0^+$ of fractional Orlicz-Sobolev spaces
Angela Alberico;
2020
Abstract
An extended version of the Maz'ya-Shaposhnikova theorem on the limit as s -> 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 \Delta2-condition, and, as shown by counterexamples, it may fail if this condition is dropped.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
