On the limit as s 0+ of fractional Orlicz-Sobolev spaces
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 2-condition, and, as shown by counterexamples, it may fail if this condition is dropped.
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