On Riesz Transforms Characterization of H1 Spaces Associated with Some Schrödinger Operators

摘要

Let Lf(x)=-Df (x)+V(x)f(x)mathcal Lf(x)=-Delta f (x)+V(x)f(x), V ≥ 0, V Î L1_loc(mathbb Rd)Vin L^1_{loc}(mathbb R^d), be a non-negative self-adjoint Schrödinger operator on mathbb Rdmathbb R^d. We say that an L 1-function f is an element of the Hardy space H1_LH^1_{mathcal L} if the maximal function $ mathcal M_{mathcal L} f(x)=suplimits_{t>0}|e^{-tmathcal L} f(x)| $ mathcal M_{mathcal L} f(x)=suplimits_{t>0}|e^{-tmathcal L} f(x)|