... supy∈Ω 1 n,λΩ2n,λ|K(x, y)| q dx 1/ r< ∞, k2= supx∈Ω2n,λΩ 1 n,λ|K(x, y)| q dy 1/ q 1/ r< ∞ (1. 8)6 Journal of Inequalities and ApplicationsProof. Let q = pr/(pr + p − r), 1/ q + 1/ q = 1. We show ... K q ( 1/ q 1/ ν)(x, y)K q/ ν(x, y)dy. (1. 10)By H¨older’s inequality with exponents λ, μ,andν,weobtainJλ(x) ≤Ω 1 n,λf (y) p ( 1/ p 1/ μ)K(x, y) q ( 1/ q 1/ ν)dy 1/ λΩ 1 n,λf (y) p dy 1/ μΩ 1 n,λK(x, ... (p, r)where1 /p= (1 t) /1 + t /q , 1/ r = (1 − t) /q .Theproofiscompleted. 8 Journal of Inequalities and Applications [11 ] Z. Zhou, Y. Hong, and C. Z. Zhou, The (p ,q) -boundedness of Riesz potential operators of variable...