Title: Boundedness for Riesz-type potential operators on Herz-Morrey spaces with variable exponent
Abstract: In this paper, the Riesz-type potential operator of variable order β (x) is shown to be bounded from the Herz-Morrey spaces M Kα,λ, where ω = (1+|x|) -γ(x) with some γ(x) > 0 and 1/q 1 (x)-1/q 2 (x) = β (x)/n when q 1 (x) is not necessarily constant at infinity.It is assumed that the exponent q 1 (x) satisfies the logarithmic continuity condition both locally and at infinity and 1 < q 1 (∞) q 1 (x) (q 1 ) + < ∞ (x ∈ R n ) .