THE BOUNDEDNESS OF CALDERÓN-ZYGMUND COMMUTATORS OF TYPE THETA ON SPACES OF HOMOGENEOUS TYPE

Tóm tắt

In this paper, we study the boundedness of Calderón-Zygmund operator and its commutator of type theta on generalized Morrey-Lorentz spaces of homogeneous type. We first modify a well-known result of Calderón-Zygmund decomposition to prove that such Calderón-Zygmund operators are of strong type (p, p) on Lebesgue spaces L^p, for every p > 1. Then by using Kolmogorov’s inequality, the standard conditions of Calderón-Zygmund operator and BMO space, we establish two pointwise estimates for sharp maximal operators. Finally, we derive the boundedness of Calderón-Zygmund operator of type theta and its commutator on generalized Morrey-Lorentz spaces of homogeneous type.