Sobolev-type inequalities on variable exponent Morrey spaces of an integral form

The aim of this paper is to deal with the boundedness of the Hardy-Littlewood maximal operator on variable exponent Morrey spaces of an integral form. As an application of the boundedness of the maximal operator, we establish Sobolev-type inequalities for Riesz potentials $$I_{\alpha (\cdot )}f$$ of variable order $$\alpha (\cdot )$$ of functions f in variable exponent Morrey spaces of an integral form.