A CHARACTERIZATION FOR FRACTIONAL INTEGRALS ON GENERALIZED MORREY SPACES

This paper concerns with the fractional integrals,which are also known as the Riesz potentials.A characterization for the boundedness of the fractional integral operators on generalized Morrey spaces will be presented.Our results can be viewed as a refinement of Nakai’s [7].     

Morrey spaces and fractional integral operators

The present paper is devoted to the boundedness of fractional integral operators in Morrey spaces defined on quasimetric measure spaces. In particular, Sobolev, trace and weighted inequalities with power weights for potential operators are established. In the case when measure satisfies the doubling condition the derived conditions are simultaneously necessary and sufficient for appropriate inequalities.