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Let L=-Δ+V be a Schrödinger operator acting on L2(Rn), n≥1, where V≢0 is a nonnegative locally integrable function on Rn. In this paper, we will first define molecules for weighted Hardy spaces HLp(w)  (0<p≤1) associated with L and establish their molecular characterizations. Then, by using the atomic decomposition and molecular characterization of HLp(w), we will show that the imaginary power Liγ is bounded on HLp(w) for n/(n+1)<p≤1, and the fractional integral operator L-α/2 is bounded from HLp(w) to HLq(wq/p), where 0<α<min{n/2,1}, n/(n+1)<p≤n/(n+α), and 1/q=1/p-α/n

The Boundedness of Some Integral Operators on Weighted Hardy Spaces Associated with Schrödinger Operators