Generalized fractional integral operators and fractional maximal operators in the framework of Morrey spaces

Abstract

The action of the generalized fractional integral operators and the generalized fractional maximal operators is investigated in the framework of Morrey spaces. A typical property of the functions which belongs to Morrey spaces under point wise multiplication by the generalized fractional integral operators and the generalized fractional maximal operators is established. The bounded ness property of the fractional integral operators on the predual of Morrey spaces is shown as well. A counterexample concerning the Fefferman-Phong inequality is given by the use of the characteristic function of the Cantor set. © 2011 American Mathematical Society.