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

A. Kucukaslan

In this paper, we prove the Spanne-type boundedness of the generalized Riesz potential operator Iρ on the generalized weighted local Morrey spaces with wq ∈ A1+q/p' for 1 < p < q < ∞ and including its the weak estimates with w ∈ A1,q for 1 < q < ∞ We also prove the Adams-type boundedness of the operator Iρ on the generalized weighted Morrey spaces with w ∈ Ap,q for 1 < p < q < ∞ and also including its the weak estimates with w ∈ A1,q for 1 < q < ∞ . 

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 14(4) (2021), pp. 111-124