Fractional Type Integral Operators on Variable Hardy Spaces

Given certain n × n invertible matrices A ₁, . . . , A _m and 0 ≦ α < n, we obtain the ({H^{p(.)}(mathbb{R}^n) to L^{q(.)}(mathbb{R}^n)}) boundedness of the integral operator with kernel ({k(x, y) = |x - A_1y|^{-alpha_1} . . . |x - A_my|^{-alpha_m}}) , where α ₁ +  . . . + α _m = n ? α and p(.), q(.) are exponent functions satisfying log-Hölder continuity conditions locally and at infinity related by ({frac{1}{q(.)} = frac{1}{p(.)} - frac{alpha}{n}}) . We also obtain the ({H^{p(.)}(mathbb{R}^n) to H^{q(.)}(mathbb{R}^n)}) boundedness of the Riesz potential operator.