Fractional integral and fractional maximal operators on generalized Fofana spaces

Abstract

Generalized Fofana spaces were recently introduced as generalizations of Fofana spaces and Nakai's generalized Morrey spaces. In this paper, we establish the boundedness properties of the following operators in these spaces: fractional integral operators, fractional maximal operators and generalized fractional integral operators. As a consequence, we obtain generalized Olsen-type inequalities involving the Riesz potential and generalized fractional integral operators.

15 pages