Estimates in L^p for magnetic Schrödinger operators

We study the magnetic Schrödinger operator H(a,V) in ℝⁿ, n ≥ 3. The L^p (1 < p < ∞) and weak-type (1,1) estimates are obtained under certain conditions, given in terms of the reverse Hölder inequality, on the magnetic field B = curl a and the electrical potential V. In particular, we show that the L^p and weak-type (1,1) estimates hold if the components of a are polynomials, and V is a nonnegative polynomial.