Boundedness of a Class of Sublinear Operators and Their Commutators on Generalized Morrey Spaces - Vagif S. Guliyev; Seymur S. Aliyev; Turhan Karaman (Abstract and Applied Analysis)
The authors study the boundedness for a large class of sublinear operator T generated by Calderón-Zygmund operator on generalized Morrey spaces Mp,φ. As an application of this result, the boundedness of the commutator of sublinear operators Ta on generalized Morrey spaces is obtained. In the case a∈BMO(ℝn), 1<p<∞ and Ta is a sublinear operator, we find the sufficient conditions on the pair (φ1,φ2) which ensures the boundedness of the operator Ta from one generalized Morrey space Mp,φ1 to another Mp,φ2. In all cases, the conditions for the boundedness of Ta are given in terms of Zygmund-type integral inequalities on (φ1,φ2), which do not assume any assumption on monotonicity of φ1,φ2 in r. Conditions of these theorems are satisfied by many important operators in analysis, in particular pseudodifferential operators, Littlewood-Paley operator, Marcinkiewicz operator, and Bochner-Riesz operator.