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

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 hl p (w) (0 < p ≤ 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 liγ is bounded on hl p (w) for n / (n + 1) < p ≤ 1,and the fractional integral operator l-α/2 is bounded from hl p (w) to hl q (wq/p),where 0 < α < m i n { n / 2,1 },n / (n + 1) < p ≤ n / (n + α),and 1 / q = 1 / p - α / n. © 2015 hua wang.