Boundedness of a Class of Sublinear Operators and Their Commutators on Generalized Morrey Spaces

WOS: 000294626900001The authors study the boundedness for a large class of sublinear operator T generated by Calderon-Zygmund operator on generalized Morrey spaces M(p,phi) As an application of this result, the boundedness of the commutator of sublinear operators T(a) on generalized Morrey spaces is obtained. In the case a is an element of BMO (R(n)), 1 < p < infinity and T(a) is a sublinear operator, we find the sufficient conditions on the pair phi(1), phi(2) which ensures the boundedness of the operator Ta from one generalized Morrey space M(p,phi 1) to another M(p,phi 2). In all cases, the conditions for the boundedness of T(a) are given in terms of Zygmund-type integral inequalities on (phi(1), phi(2)), which do not assume any assumption on monotonicity of phi(1), phi(2) 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.Science Development Foundation [01/023]; Ahi Evran UniversityAhi Evran University [BAP FBA-10-05]; Scientific and Technological Research Council of TurkeyTurkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK) [110T695]The authors express their thank to prof A. Serbetci for helpful comments on the paper of this paper. The authors would like to express their gratitude to the referees for his very valuable comments and suggestions. The research of V. Guliyev was partially supported by the grant of Science Development Foundation under the President of the Republic of Azerbaijan project no-01/023. The research of V. Guliyev and T. Karaman was partially supported by the grant of 2010-Ahi Evran University Scientific Research Projects (BAP FBA-10-05) and by the Scientific and Technological Research Council of Turkey (TUBITAK Project no: 110T695)