An elementary proof of sharp Sobolev embeddings

DOI10.1090/S0002-9939-01-06060-9zbMath0990.46022OpenAlexW1880169946WikidataQ116548171 ScholiaQ116548171MaRDI QIDQ2758994

Luboš Pick, Jan Malý

Publication date: 10 December 2001

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-01-06060-9

zbMATH Keywords

Sobolev embeddingsOrlicz spacesTrudinger inequalityrearrangement-invariant Banach function spacesweak inequalitiesGagliardo-Nirenberg embedding

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) Inequalities involving derivatives and differential and integral operators (26D10)

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• Weak-\(L^\infty\) and BMO
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• Convolution operators and L(p, q) spaces
• Imbedding theorems of Sobolev type in potential theory.
• A note on limiting cases of sobolev embeddings and convolution inequalities
• A sharp embedding theorem for Orlicz-Sobolev spaces
• Sobolev inequalities in disguise
• On the sharpness of a limiting case of the Sobolev imbedding theorem

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