Boundedness for fractional Hardy-type operator on variable-exponent Herz–Morrey spaces

Source abstract

In this article, the fractional Hardy-type operator of variable order β(x) is shown to be bounded from the variable-exponent Herz–Morrey spaces MK˙p1,q1(⋅)α(⋅),λ(Rn) into the weighted space MK˙p2,q2(⋅)α(⋅),λ(Rn,ω), where α(x)∈L∞(Rn) is log-Hölder continuous both at the origin and at infinity, ω=(1+|x|)−γ(x) with some γ(x)>0, and 1/q1(x)−1/q2(x)=β(x)/n when q1(x) is not necessarily constant at infinity.