Generalized fractional integrals in the vanishing generalized weighted local and global Morrey spaces

In this paper, we prove the boundedness of generalized fractional integral operators I rho in the vanishing generalized weighted Morrey-type spaces, such as vanishing generalized weighted local Morrey spaces and vanishing generalized weighted global Morrey spaces by using weighted Lp estimates over balls.In more detail, we obtain the Spanne-type boundedness of the generalized fractional integral operators I rho in the vanishing generalized weighted local Morrey spaces with wq E A1+ q p ' the vanishing generalized weighted local Morrey spaces to the vanishing generalized weighted weak local Morrey spaces with w E A1,q for p = 1,1 < q < oo. We also prove the Adams-type boundedness of the generalized fractional integral operators I rho in the vanishing generalized weighted global Morrey spaces with w E Ap,q for 1 < p < q < oo and from the vanishing generalized weighted global Morrey spaces to the vanishing generalized weighted weak global Morrey spaces with w E A1,q for p = 1,1 < q < oo. The our all weight functions belong to Muckenhoupt-Weeden classes Ap,q. for 1 < p < q < oo, and from