Variable exponent Campanato spaces

H. Rafeiro, S. Samko

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)

Abstract

We study variable exponent Campanato spaces Lp(·),λ(·)(X) on spaces of homogeneous type. We prove an embedding result between variable exponent Campanato spaces. We also prove that these spaces are equivalent, up to norms, to variable exponent Morrey spaces Lp(·),λ(·) (X) with λ+ < 1 and variable exponent Hölder spaces Hα(·)(X) with λ- > 1. In the setting of an arbitrary quasimetric measure spaces, we introduce the log-Hölder condition for p(x) with the distance d(x, y) replaced by μB(x, d(x, y)), which provides a weaker restriction on p(x) in the general setting and show that some basic facts for variable exponent Lebesgue spaces hold without the assumption that X is homogeneous or even Ahlfors lower or upper regular. However, the main results for Campanato spaces are proved in the setting of homogeneous spaces X. Bibliography: 34 titles.

Original languageEnglish
Pages (from-to)143-164
Number of pages22
JournalJournal of Mathematical Sciences
Volume172
Issue number1
DOIs
Publication statusPublished - Jan 2011
Externally publishedYes

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Applied Mathematics

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