On potentials of distributions in Orlicz-Hardy type spaces on the Heisenberg group

Abstract

In this work, we introduce Orlicz-Hardy type spaces and Orlicz-Calderón Hardy type spaces on the Heisenberg group $\mathbb{H}^{n}$ and study the relationship between them by means of the Heisenberg sub-Laplacian $\mathcal{L}$. More precisely, we show, under suitable assumptions, that every distribution in the Orlicz-Hardy space $H^Φ(\mathbb{H}^{n})$ can be represented uniquely as the sub-Laplacian of a function in an appropriate Orlicz-Calderón Hardy space. In this way, for any $f \in H^Φ(\mathbb{H}^{n})$, we obtain a uniqueness and solvability result for the equation $\mathcal{L}F=f$.