Sharp embeddings of Besov spaces involving only logarithmic smoothness

• Autores: António M. Caetano, Amiran Gogatishvili , Bohumír Opic
• Localización: Journal of approximation theory, ISSN 0021-9045, Vol. 152, Nº 2, 2008, págs. 188-214
• Idioma: inglés
• DOI: 10.1016/j.jat.2007.12.003
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• Resumen

  • We use Kolyada's inequality and its converse form to prove sharp embeddings of Besov spaces (involving the zero classical smoothness and a logarithmic smoothness with the exponent ß) into Lorentz-Zygmund spaces. We also determine growth envelopes of spaces . In distinction to the case when the classical smoothness is positive, we show that we cannot describe all embeddings in question in terms of growth envelopes.