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

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 $s \to 0^{+}$ of fractional Orlicz-Sobolev spaces

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

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

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

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

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

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