Reduction theorems for Sobolev embeddings into the spaces of Hölder, Morrey and Campanato type

DOI10.1002/mana.201500043zbMath1365.46025OpenAlexW2341522473MaRDI QIDQ2832676

Miloslav Holík

Publication date: 11 November 2016

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.201500043

zbMATH Keywords

Sobolev embeddingsreduction operatorrearrangement-invariant function spacesPólya-Szegő principlegeneralized CampanatoMorrey and Hölder spaces

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35)

Related Items

Sobolev embeddings, rearrangement-invariant spaces and Frostman measures

Cites Work

• Optimal Gaussian Sobolev embeddings
• Sobolev embeddings into spaces of Campanato, Morrey, and Hölder type
• Sobolev embeddings into BMO, VMO, and \(L_{\infty}\)
• Optimal Sobolev imbeddings involving rearrangement-invariant quasinorms
• Higher-order Sobolev embeddings and isoperimetric inequalities
• Embeddings of Sobolev-type spaces into generalized Hölder spaces involving \(k\)-modulus of smoothness
• Non-compact and sharp embeddings of logarithmic Bessel potential spaces into Hölder-type spaces
• On functions of bounded mean oscillation
• Optimal Sobolev imbeddings
• On the modulus of continuity of weakly differentiable functions