Boundedness of functions in fractional Orlicz-Sobolev spaces

Abstract

A necessary and sufficient condition for fractional Orlicz-Sobolev spaces to be continuously embedded into L infinity(Rn) 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 infinity(Rn) fails. They also augment a classical embedding theorem for standard fractional Sobolev spaces.(c) 2023 Elsevier Ltd.

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Keywords

• Fractional Orlicz-Sobolev spaces
• Boundedness of functions
• Smooth approximation
• Orlicz spaces
• Orlicz-Lorentz spaces
• Rearrangement-invariant spaces