Generalized fractional integral operators on variable exponent Morrey type spaces over metric measure spaces

Abstract

We prove the boundedness of generalized fractional integral operators I_{\rho,\tau} on variable exponent Morrey type spaces \mathcal{L}^{p(\cdot),\omega,\theta}(X) over non-doubling metric measure spaces X , where both \rho(x,r) and \omega(x,r) depend on x \in X . Our result extends the recent results by the authors.