The Spanne-type result in the vanishing generalized weighted local Morrey spaces

A. Kucukaslan

In this paper, we prove the Spanne-type boundedness of the generalized fractional maximal operator Mρ from the vanishing generalized weighted local Morrey spaces VMp,φ1{x0}(ℝn, wp) to another one VMq,φ2{x0}(ℝn, wq) with wq ∈ A1+q/p', and from the vanishing generalized weighted local Morrey spaces VMp,φ1{x0}(ℝn, w) to the vanishing generalized weighted weak local Morrey spaces VWMq,φ2{x0}(ℝn, wq) with wq ∈ A1,q, where φ1, φ2 ∈ Mloc class. Also, we get a new theorem for the Spanne-type result of the generalized fractional maximal operator Mρ from the vanishing generalized Morrey spaces VMp,φ1(ℝn) to VMq,φ2(ℝn), including weak estimates. The all weight functions belong to Muckenhoupt -Weeden classes Ap,q. 

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 16,  supplement issue 4 (2023), pp. 177-187