CHARACTERIZATIONS FOR THE FRACTIONAL INTEGRAL OPERATOR AND ITS COMMUTATORS IN GENERALIZED WEIGHTED MORREY SPACES ON CARNOT GROUPS


Creative Commons License

Guliyev V. S. , Ekincioglu İ.

JOURNAL OF MATHEMATICAL INEQUALITIES, vol.15, no.1, pp.151-171, 2021 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 1
  • Publication Date: 2021
  • Doi Number: 10.7153/jmi-2021-15-14
  • Journal Name: JOURNAL OF MATHEMATICAL INEQUALITIES
  • Journal Indexes: Science Citation Index Expanded, Scopus, zbMATH
  • Page Numbers: pp.151-171
  • Keywords: Cannot group, fractional integral operator, generalized weighted Morrey space, commutator, BMO, HIGHER-ORDER COMMUTATORS, HARDY-LITTLEWOOD, MAXIMAL OPERATOR, BESOV-SPACES, NORM INEQUALITIES, LIE-GROUPS, RIESZ

Abstract

In this paper, we shall give a characterization for the strong and weak type Spanne type boundedness of the fractional integral operator I-alpha, 0 < alpha < Q on Carrot group G on generalized weighted Morrey spaces M-p,M-phi (G,w), respectively, where Q is the homogeneous dimension of G. Also we give a characterization for the Spanne type boundedness of the commutator operator [b,I-alpha] on generalized weighted Morrey spaces.