Two-type estimates for the boundedness of generalized Riesz potential operator in the generalized weighted local Morrey spaces

Abstract

In this paper, we prove the Spanne-type boundedness of the generalized Riesz potential operator $I_{\rho}$ on the generalized weighted local Morrey spaces with $w^{q} \in A_{1+\frac{q}{p'}}$ for $1 \le p \le q \le \infty $ and including its the weak estimates with $w \in A_{1,q}$ for $1\le q\le\infty$. We also prove the Adams-type boundedness of the operator $I_{\rho}$ on the generalized weighted Morrey spaces with $ w \in A_{p,q}$ for $1\le p\le q \le \infty$ and also including its the weak estimates with $w \in A_{1,q}$ for $1\le q\le \infty$.