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arXiv · 2002.05449

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

Angela Alberico·Andrea Cianchi·Luboš Pick·Lenka Slavíková
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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 $\Delta_2$-condition, and, as shown by counterexamples, it may fail if this condition is dropped.

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Angela Alberico, Andrea Cianchi, Luboš Pick, Lenka Slavíková. 2020-02-13. On the limit as $s\to 0^+$ of fractional Orlicz-Sobolev spaces. https://arxiv.org/abs/2002.05449

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