Convolution operators and variable Hardy spaces on the Heisenberg group

Let H^n be the Heisenberg group. For 0 < Q=2n+2 and N N we consider exponent functions p (): H^n (0, +), which satisfies H\"older conditions, such that QQ+N < p- p () p+ < Q. In this article we prove the H^p () (H^n) L^q () (H^n) and H^p () (H^n) H^q () (H^n) boundedness of convolution operators with kernels of type (, N) on H^n, where 1q () = 1p () - Q. In particular, the Riesz potential on H^n satisfies such estimates.