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arXiv · 2302.10839

Inclusion relations among fractional Orlicz-Sobolev spaces and a Littlewood-Paley characterization

Dominic Breit·Andrea Cianchi
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Abstract

Embeddings among fractional Orlicz-Sobolev spaces with different smoothness are characterized. The equivalence of their Gagliardo-Slobodeckij norms to norms defined via Littlewood-Paley decompostions, via oscillations, or via Besov type difference quotients is also established. These equivalences, of independent interest, are a key tool in the proof of the relevant embeddings. They also rest upon a new optimal inequality for convolutions in Orlicz spaces.

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Dominic Breit, Andrea Cianchi. 2023-02-21. Inclusion relations among fractional Orlicz-Sobolev spaces and a Littlewood-Paley characterization. https://arxiv.org/abs/2302.10839

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