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arXiv · 2207.10597

Boundedness of functions in fractional Orlicz-Sobolev spaces

Angela Alberico·Andrea Cianchi·Luboš Pick·Lenka Slavíková
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Abstract

A necessary and sufficient condition for fractional Orlicz-Sobolev spaces to be continuously embedded into $L^\infty(\mathbb R^n)$ is exhibited. Under the same assumption, any function from the relevant fractional-order spaces is shown to be continuous. Improvements of this result are also offered. They provide the optimal Orlicz target space, and the optimal rearrangement-invariant target space in the embedding in question. These results complement those already available in the subcritical case, where the embedding into $L^\infty(\mathbb R^n)$ fails. They also augment a classical embedding theorem for standard fractional Sobolev spaces.

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Angela Alberico, Andrea Cianchi, Luboš Pick, Lenka Slavíková. 2022-07-21. Boundedness of functions in fractional Orlicz-Sobolev spaces. https://arxiv.org/abs/2207.10597

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