Besov and Hardy spaces associated with the Schrödinger operator on the Heisenberg group
Consider the Schrödinger operator \(L=-\Delta_{{\mathbb{H}}^n}+V\) on the Heisenberg group \( \mathbb{H}^n\), where \(\Delta_{\mathbb{H}^n}\) is the sub-Laplacian on \(\mathbb{H}^n\) and \(V\) is in the reverse Hölder class \(B_q\) with \(q \geq n+1\). In this paper, the Besov space \(\dot{B}_{1,1}^{0, L}\) and the Hardy space \(H_{L}^{1}\) associated with \(L\) are defined by the heat semigroup and the Littlewood-Paley area function, respectively, and then characterized in terms of atomic and molecular decomposition. Consequently, it is shown that \(\dot{B}_{1,1}^{0, L}\) is a subspace of \(H_{L}^{1}\).
scientific article; zbMATH DE number 6370382
scientific article