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

Abstract

In this paper, we study the boundedness of Calderón-Zygmund operator  and its commutator  of type  on generalized Morrey-Lorentz spaces , where  is a space of homogeneous type. We first modify a well-known result of Calderón-Zygmund decomposition to prove that Calderón-Zygmund operators are of strong type  on , for every  (see Lemma 2.1, Lemma 2.2, and Lemma 2.3). By using Kolmogorov’s inequality, conditions of Calderón-Zygmund operators, and BMO spaces, we establish two pointwise estimates for sharp maximal operators (see Lemma 2.6 and Lemma 2.8). Finally, we derive the boundedness of and  on  (see Theorem 3.1).