In this paper, we prove the Spanne-Guliyev type boundedness of the generalized fractional integral operator I ρ from the vanishing generalized local Morrey spaces V LM {x 0 } p,ϕ 1 to V LM {x 0 } q,ϕ 2 , 1 < p < q < ∞, and from the space V LM {x 0 } 1,ϕ 1 to the weak space V W LM {x 0 } q,ϕ 2 , 1 < q < ∞. We also prove the Adams-Guliyev type boundedness of the operator I ρ from the vanishing generalized Morrey spaces V M p,ϕ

We characterize associate spaces of generalized weighted weak-Lorentz spaces and use this characterization to study embeddings between these spaces.

In this paper we define a new class of functions called local Morrey-Lorentz spaces M loc p,q;λ (R n ), 0 < p, q ≤ ∞ and 0 ≤ λ ≤ 1. These spaces generalize Lorentz spaces suchis trivial, and in the limiting case λ = 1, the space M loc p,q;1 (R n ) is the classical Lorentz spaceWe show that for 0 < q ≤ p < ∞ and 0 < λ ≤

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