An estimate on the heat kernel of Schrödinger operators with non-negative potentials on nilpotent Lie groups and its applications

Abstract

Abstract In this paper we investigate the heat kernel of the Schrödinger operator L = - Δ G + W $L=-\Delta _G+W$ on the nilpotent Lie group G, where Δ G is the sub-Laplacian on G and the non-negative potential W belongs to the reverse Hölder class B q 1 . The main aim of the paper is to give a pointwise estimate for the heat kernel of Schrödinger operators with non-negative potentials on the nilpotent Lie group G. As its applications, we obtain the Lp estimates for parabolic Schrödinger operators with certain non-negative potentials.