Vanishing Sobolev Integrability and Trudinger Exponential Integrability for Fractional Operators in Morrey-Orlicz Spaces

Abstract

Our aim in this paper is to establish the vanishing Sobolev integrability for fractional maximal functions and Riesz potentials in Morrey-Orlicz spaces. The size of the exceptional sets is evaluated by using the Hausdorff measure. In the borderline case we discuss Trudinger-type exponential integrability for fractional maximal functions and Riesz potentials. We also discuss the sharpness of our results.