Variable Calder\'on-Hardy spaces on the Heisenberg group

Let Hⁿ be the Heisenberg group and $Q = 2n+2$. For 1 < q < ∞, γ > 0 and an exponent function p(·) on Hⁿ, which satisfy log-H\"older conditions, with 0 < p₋ ≤ p₊ < ∞, we introduce the variable Calder\'on-Hardy spaces Hp(·)q, γ(Hⁿ), and show for every f ∈ Hp(·)(Hⁿ) that the equation \[ L F = f \] has a unique solution F in Hp(·)q, 2(Hⁿ), where L is the sublaplacian on Hⁿ, 1 < q < n+1/n and Q (2 + Q/q)⁻¹ < p.