Interpolation inequality of logarithmic type in abstract Besov spaces and an application to semilinear evolution equations

Toshitaka Matsumoto, Takayoshi Ogawa

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

An abstract version of Besov spaces is introduced by using the resolvent of nonnegative operators. Interpolation inequalities with respect to abstract Besov spaces and generalized Lorentz spaces are obtained. These inequalities provide a generalization of Sobolev inequalities of logarithmic type. Uniqueness problems to abstract semilinear evolution equations are also discussed.

Original languageEnglish
Pages (from-to)1810-1828
Number of pages19
JournalMathematische Nachrichten
Volume283
Issue number12
DOIs
Publication statusPublished - 2010 Dec 1

Keywords

  • Abstract Besov space
  • Limiting interpolation inequality
  • Lorentz spaces
  • The K-method
  • Uniqueness problems for semilinear evolution equations

ASJC Scopus subject areas

  • Mathematics(all)

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