On Sobolev theorem for higher commutators of fractional integrals in grand variable Herz spaces

Abstract

The higher order commutators of fractional integral operator Iζ(⋅),Vm of variable order is shown to be bounded from the grand variable Herz spaces K̇p(⋅)a(⋅),u,θ(Rn) into the weighted space K̇ρ,q(⋅)a(⋅),u,θ(Rn), where ρ=(1+|z1|)−λ and 1q(z)=1p(z)−β(z)n when p(z) is not necessarily constant at infinity.