Anisotropic maximal commutator and commutator of anisotropic maximal operator on Lorentz spaces
Transactions of National Academy of Sciences of Azerbaijan. Series of Physical-Technical and Mathematical Sciences, vol.44, no.4, pp.5-12, 2024 (Scopus)
- Publication Type: Article / Article
- Volume: 44 Issue: 4
- Publication Date: 2024
- Journal Name: Transactions of National Academy of Sciences of Azerbaijan. Series of Physical-Technical and Mathematical Sciences
- Journal Indexes: Scopus
- Page Numbers: pp.5-12
- Keywords: anisotropic maximal operator, BMO spaces, commutator, Lorentz spaces
- Ankara University Affiliated: Yes
Abstract
In this paper we consider the anisotropic maximal commutator Mbd and the commutator of the anisotropic maximal operator [b, Md] on the Lorentz spaces Lp,q (ℝn). We obtain necessary and sufficient conditions for the boundedness of the operators Mbd and[b, Md] on Lp,q (ℝn) when b belongs to the bounded mean oscillation space BMO(ℝn), whereby some new characterizations for certain subclasses of BMO(ℝn) are obtained.