Fractional integral operators in nonhomogeneous spaces

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.