Maximal inequalities and Riesz transform estimates on Lp spaces for magnetic Schrödinger operators I

The paper concerns the magnetic Schrödinger operator H(a,V ) = n j=1( 1 i ∂ ∂xj − aj )2 + V on Rn. Under certain conditions, given in terms of the reverse Hölder inequality on the magnetic field and the electric potential, we prove some Lp estimates on the Riesz transforms of H and we establish some related maximal inequalities. © 2009 Elsevier Inc. All rights reserved.