Sobolev embeddings into spaces of Campanato, Morrey, and Hölder type |
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| Authors: | Andrea Cianchi |
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| Institution: | a Dipartimento di Matematica e Applicazioni per l'Architettura, Università di Firenze, Piazza Ghiberti 27, 50122 Firenze, Italy
b Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic |
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| Abstract: | Necessary and sufficient conditions on a rearrangement-invariant Banach function space X(Q) on a cube Q in  , n?2, are given for the corresponding Sobolev space W1X(Q) to be continuously embedded into (generalized) Campanato, Morrey, or Hölder spaces. The optimal such r.i. spaces X(Q) are found. As a by-product, sharp inclusion relations are proved among Campanato, Morrey, and Hölder type spaces. |
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| Keywords: | Generalized Campanato spaces Morrey spaces Hö lder spaces Sobolev embeddings Rearrangement-invariant spaces Optimal domain |
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