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.