Abstract
Our aim in this paper is to establish variable exponent weighted norm inequalities for generalized Riesz potentials on the unit ball via norm inequalities in variable exponent non-homogeneous central Herz–Morrey spaces on the unit ball. As an application, we shall show Sobolev-type integral representation for a ?1 -function on ℝ?∖{0} which vanishes outside the unit ball.
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