Mixed norms and Sobolev type inequalities

Volume 72 / 2006

V. I. Kolyada Banach Center Publications 72 (2006), 141-160 MSC: Primary 46E30, 46E35. DOI: 10.4064/bc72-0-10

Abstract

We study mixed norm spaces that arise in connection with embeddings of Sobolev and Besov spaces. We prove Sobolev type inequalities in terms of these mixed norms. Applying these results, we obtain optimal constants in embedding theorems for anisotropic Besov spaces. This gives an extension of the estimate proved by Bourgain, Brezis and Mironescu for isotropic Besov spaces.

Authors

  • V. I. KolyadaDepartment of Mathematics
    Karlstad University
    Universitetsgatan 1
    651 88 Karlstad, Sweden
    e-mail

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