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

Let L = -Delta + V be a Schrodinger operator acting on L-2(R-n), n >= 1, where V not equivalent to 0 is a nonnegative locally integrable function on R-n In this paper, we will first define molecules for weighted Hardy spaces H-L(P)(w) ( 0 < p <= 1) associated with.. 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 <= 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 <= n/(n+alpha), and 1/q = 1/p-alpha/n.