Commutator of anisotropic maximal function with BMO functions on total anisotropic morrey spaces

Abasova G. A., Omarova M. N.

Transactions Issue Mathematics, Azerbaijan National Academy of Sciences, vol.43, no.1, pp.3-15, 2023 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 43 Issue: 1
  • Publication Date: 2023
  • Journal Name: Transactions Issue Mathematics, Azerbaijan National Academy of Sciences
  • Journal Indexes: Scopus
  • Page Numbers: pp.3-15
  • Keywords: Anisotropic maximal operator, BMO spaces, Commutator, Total anisotropic Morrey spaces
  • Azerbaijan State University of Economics (UNEC) Affiliated: No

Abstract

In this paper, we consider the total anisotropic Morrey spaces Ldp, λ, μ (Rn) introduced by Guliyev in [22] in the isotropic case d = (1, ..., 1). These spaces generalize the anisotropic Morrey spaces so that Ldp, λ, λ(Rn) ≡ Ldp, λ(Rn) and the modified anisotropic Morrey spaces so that Ldp, λ, 0(Rn) = Ldp, λ (Rn). We give basic properties of the spaces Ldp, λ, λ (Rn) and study some embeddings into the Morrey space Ldp, λ, μ (Rn). We also give necessary and sufficient conditions for the boundedness of the anisotropic maximal commutator operator Mbd and commutator of anisotropic maximal operator [b, Md] on Ldp,λ, μ (Rn). We obtain some new characterizations for certain subclasses of BMO(Rrn).