Sublinear operators with a rough kernel generated by fractional integrals and local Campanato space estimates for commutators with rough kernel on generalized local Morrey spaces

Gurbuz F.

INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS & STATISTICS, vol.56, no.3, pp.52-62, 2017 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 56 Issue: 3
  • Publication Date: 2017
  • Journal Name: INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS & STATISTICS
  • Journal Indexes: Emerging Sources Citation Index (ESCI), zbMATH
  • Page Numbers: pp.52-62
  • Keywords: Sublinear operator, fractional integral operator, rough kernel, generalized local Morrey space, commutator, local Campanato space, SINGULAR-INTEGRALS
  • Ankara University Affiliated: Yes

Abstract

In this paper, we consider the norm inequalities for sublinear operators with a rough kernel generated by fractional integrals and commutators on generalized local Morrey spaces including their weak versions under generic size conditions which are satisfied by most of the operators in harmonic analysis. As an example to the conditions of these theorems to be satisfied, we can consider the Marcinkiewicz operator.