On fractional Orlicz–Sobolev spaces
Copyright policy )On fractional Orlicz–Sobolev spaces
AbstractSome recent results on the theory of fractional Orlicz–Sobolev spaces are surveyed. They concern Sobolev type embeddings for these spaces with an optimal Orlicz target, related Hardy type inequalities, and criteria for compact embeddings. The limits of these spaces when the smoothness parameter$$s\in (0,1)$$s∈(0,1)tends to either of the endpoints of its range are also discussed. This note is based on recent papers of ours, where additional material and proofs can be found.
- National Research Council Italy
- University of Florence Italy
- Charles University Czech Republic
- New York University Italy
- Istituto per le Applicazioni del Calcolo Mauro Picone Italy
Algebra and Number Theory, fractional Orlicz-Sobolev spaces, Orlicz spaces · Rearrangement-invariant spaces, limits of fractional seminorms, Orlicz spaces, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.), compact embeddings, rearrangement-invariant spaces, Sobolev embeddings, Fractional Orlicz{Sobolev spaces; Sobolev embeddings; compact embeddings; limits of fractional seminorms; Orlicz spaces; rearrangement-invariant spaces., Compact embeddings, Fractional Orlicz–Sobolev spaces, Sobolev embeddings, Compact embeddings, Limits of fractional seminorms, Orlicz spaces, Rearrangement-invariant spaces, Fractional Orlicz–Sobolev spaces, Limits of fractional seminorms, Research exposition (monographs, survey articles) pertaining to functional analysis, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, Mathematical Physics, Analysis
Algebra and Number Theory, fractional Orlicz-Sobolev spaces, Orlicz spaces · Rearrangement-invariant spaces, limits of fractional seminorms, Orlicz spaces, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.), compact embeddings, rearrangement-invariant spaces, Sobolev embeddings, Fractional Orlicz{Sobolev spaces; Sobolev embeddings; compact embeddings; limits of fractional seminorms; Orlicz spaces; rearrangement-invariant spaces., Compact embeddings, Fractional Orlicz–Sobolev spaces, Sobolev embeddings, Compact embeddings, Limits of fractional seminorms, Orlicz spaces, Rearrangement-invariant spaces, Fractional Orlicz–Sobolev spaces, Limits of fractional seminorms, Research exposition (monographs, survey articles) pertaining to functional analysis, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, Mathematical Physics, Analysis
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