Convolution operators and variable Hardy spaces on the Heisenberg group

Let Hⁿ be the Heisenberg group. For 0 ≤ α < Q=2n+2 and N ∈ N we consider exponent functions p(·) : Hⁿ → (0, +∞), which satisfies H\"older conditions, such that Q/Q+N < p₋ ≤ p(·) ≤ p₊ < Q/α. In this article we prove the Hp(·)(Hⁿ) → Lq(·)(Hⁿ) and Hp(·)(Hⁿ) → Hq(·)(Hⁿ) boundedness of convolution operators with kernels of type (α, N) on Hⁿ, where 1/q(·) = 1/p(·) - α/Q. In particular, the Riesz potential on Hⁿ satisfies such estimates.