Sharp embeddings of Besov spaces with logarithmic smoothness

• Autores: Petr Gurka, Bohumír Opic
• Localización: Revista matemática complutense, ISSN-e 1988-2807, ISSN 1139-1138, Vol. 18, Nº 1, 2005, págs. 81-110
• Idioma: inglés
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• Resumen

  • We prove sharp embeddings of Besov spaces B with the classical smoothness a and a logarithmic smoothness a into Lorentz-Zygmund spaces. Our results extend those with a = 0, which have been proved by D. E. Edmunds and H. Triebel. On page 88 of their paper (Math. Nachr. 207 (1999), 79-92) they have written: "Nevertheless a direct proof, avoiding the machinery of function spaces, would be. desirable." In our paper we give such a proof even in a more general context. We cover both the sub-limiting and the limiting cases and we determine growth envelopes of Besov spaces with logarithmic smoothness.