## Abstract

We study variable exponent Campanato spaces L^{p}(·),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 L^{p(·),λ(·)} (X) with λ_{+} < 1 and variable exponent Hölder spaces H^{α(·)}(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 language | English |
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Pages (from-to) | 143-164 |

Number of pages | 22 |

Journal | Journal of Mathematical Sciences |

Volume | 172 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 2011 |

Externally published | Yes |

## ASJC Scopus subject areas

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