Equivalence of norms of the generalized fractional integral operator and the generalized fractional maximal operator on the generalized weighted Morrey spaces


Kucukaslan A.

Annals of Functional Analysis, vol.11, no.4, pp.1007-1026, 2020 (Journal Indexed in SCI Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 4
  • Publication Date: 2020
  • Doi Number: 10.1007/s43034-020-00066-w
  • Title of Journal : Annals of Functional Analysis
  • Page Numbers: pp.1007-1026
  • Keywords: Generalized fractional integral operator, Generalized fractional maximal operator, Generalized weighted Morrey spaces, Muckenhoupt class, Sharp maximal function

Abstract

© 2020, Tusi Mathematical Research Group (TMRG).The goal of this paper is to characterize the local sharp estimate (Iρf)#(x)≤CMρf(x) and by using this inequality to get necessary and sufficient conditions on the triple functions (φ, ρ, ω) which satisfy the equivalence of norms of the generalized fractional integral operator Iρ and the generalized fractional maximal operator Mρ on the generalized weighted Morrey spaces Mp,φ(Rn, ω) and generalized weighted central Morrey spaces M˙ p,φ(Rn, ω) , when ω∈ A∞-Muckenhoupt class.