Fractional Orlicz-Sobolev embeddings

Abstract

The optimal Orlicz target space is exhibited for embeddings of fractional-order Orlicz-Sobolev spaces in R-n. An improved embedding with an Orlicz-Lorentz target space, which is optimal in the broader class of all rearrangement-invariant spaces, is also established.

Both spaces of order s is an element of (0, 1), and higher-order spaces are considered. Related Hardy type inequalities are proposed as well. (C) 2020 Elsevier Masson SAS.

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Keywords

• Fractional Orlicz-Sobolev spaces
• Sobolev embeddings
• Hardy inequalities
• Orlicz spaces
• Rearrangement-invariant spaces