The boundedness of some integral operators on weighted Hardy spaces associated with Schrödinger operators (Q901655)

Summary: Let \(L=-\Delta+V\) be a Schrödinger operator acting on \(L^2(\mathbb R^n)\), \(n\geq 1\), where \(V\not\equiv 0\) is a nonnegative locally integrable function on \(\mathbb R^n\). In this paper, we will first define molecules for weighted Hardy spaces \(H_L^p(w)\) \((0<p\leq 1)\) associated with \(L\) and establish their molecular characterizations. Then, by using the atomic decomposition and molecular characterization of \(H_L^p(w)\), we will show that the imaginary power \(L^{i\gamma}\) is bounded on \(H_L^p(w)\) for \(n/(n+1)<p\leq 1\), and the fractional integral operator \(L^{-\alpha/2}\) is bounded from \(H_L^p(w)\) to \(H_L^q(w^{q/p})\), where \(0<\alpha<\min\{n/2,1\},n/(n+1)<p\leq n/(n+\alpha)\), and \(1/q=1/p-\alpha/n\).