Fractional integral operators in nonhomogeneous spaces
Gunawan H.a, Sawano Y.b, Sihwaningrum I.a
a Department of Mathematics, Bandung Institute of Technology, Indonesia
b Department of Mathematics, Gakushuin University, Japan
Abstract
We discuss here the boundedness of the fractional integral operator I a and its generalized version on generalized nonhomogeneous Morrey spaces. To prove the boundedness of Ia, we employ the boundedness of the so-called maximal fractional integral operator Ia,k*. In addition, we prove an Olsen-type inequality, which is analogous to that in the case of homogeneous type. © Australian Mathematical Publishing Association Inc. 2009.
Author keywords
Indexed keywords
Fractional integral operators,Generalized Morrey spaces,Nondoubling measures,Olsens inequality