Maximal function characterizations of Hardy spaces associated with magnetic Schrödinger operators (Q2890539)

From the authors' abstract: Let \(A=-(\nabla- i\overset\rightharpoonup a)+ V\) be a magnetic Schrödinger operator on \(L^2(\mathbb{R}^n)\), \(n\geq 2\), where \(\overset\rightharpoonup a\in L^2_{\text{loc}}(\mathbb{R}^n,\mathbb{R}^n)\) and \(0\leq V\in L^1_{\text{loc}}(\mathbb{R}^n)\). The authors establish the equivalent characterization of the Hardy space \(H^p_A(\mathbb{R}^n)\) for \(p\in (0,1]\), defined by the Lusin area function associated with \(A\), in terms of the radical maximal functions and the non-tangential maximal functions associated with \(\{e^{-t^2A}\}_{t> 0}\) and \(\{e^{-t\sqrt{A}}\}_{t> 0}\), respectively. This gives an affirmative answer to an open problem of \textit{X. T. Duong}, \textit{O. El Maati} and \textit{L. Yan} [Ark. Mat. 44, No. 2, 261--275 (2006; Zbl 1172.35370)]. The boundedness of the Riesz transform \(L_kA^{-1/2}\), \(k\in \{1,\dots, n\}\), from \(H^p_A(\mathbb{R}^n)\) to \(L^p(\mathbb{R}^n)\) is also presented, where \(L_k\) is the closure of \({\partial\over\partial x_k}- ia_k\) in \(L^2(\mathbb{R}^n)\) and \(p\in (0,1]\).