Boundedness of Commutators on Generalized Morrey Spaces

Abstract

Wainger S.etc (Wainger, S. 1965.) had studied the boundedness of the operators T on ) ( n q R L . Chanillo (Chanillo, S. 1984.) developed weighted ) ( n q R L theory by virtue of a basal lemma which will be mentioned later. Garcia-Cuerva J. etc (Garcia-Cuerva, J. , Harboure, E. , Segovia, C. and Torrea, J. L.) obtained the boundedness of higher-order commutators on weighted ) ( n q R L . Morrey (Morrey, C. B. 1938.) proposed the classical Morrey spaces when he studied the properties of local solutions of second order elliptic equations. In Ref. (Mizuhara T.. 1991.) Mizuhara introduced the following generalized Morrey spaces. Let be positive increasing functions on , 0 satisfying ) ( ) 2 ( r D r for any 0 r , where 1 D is a constant independent of r . Definition 1 (Mizuhara T. 1991.) For p 1 ,we define the generalized Morrey spaces as the following