Sublinear operators with rough kernel generated by Calderon-Zygmund operators and their commutators on generalized local Morrey spaces

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Balakishiyev A. S., Guliyev V. S., Gurbuz F., ŞERBETÇİ A.

JOURNAL OF INEQUALITIES AND APPLICATIONS, vol.2015, pp.1-18, 2015 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2015
  • Publication Date: 2015
  • Doi Number: 10.1186/s13660-015-0582-y
  • Journal Name: JOURNAL OF INEQUALITIES AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1-18
  • Keywords: sublinear operator, Calderon-Zygmund operator, rough kernel, generalized local Morrey space, commutator, local Campanato space, SINGULAR INTEGRAL-OPERATORS, SUFFICIENT CONDITIONS, DIRICHLET PROBLEM, ELLIPTIC-EQUATIONS, MAXIMAL OPERATOR, BOUNDEDNESS, HARDY
  • Ankara University Affiliated: Yes

Abstract

In this paper, we will study the boundedness of a large class of sublinear operators with rough kernel T-Omega on the generalized local Morrey spaces LM rho,phi{x0}, for s' <= p, p not equal 1 or p < s, where Omega is an element of L-s(Sn-1) with s > 1 are homogeneous of degree zero. In the case when b is an element of LCp,lambda{x0} is a local Campanato spaces, 1