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) is an element of A(1+q/p') for 1 < p < q < infinity and including its the weak estimates with w is an element of A(1, q) for 1 < q < infinity. We also prove the Adams-type boundedness of the operator I-rho, on the generalized weighted Morrey spaces with w is an element of A(p,q) for 1 < p < q < infinity and also including its the weak estimates with w is an element of A(1,q) for 1 < q < infinity.