Orlicz estimates for parabolic Schrödinger operators with non-negative potentials on nilpotent Lie groups

Abstract

In this paper, we study the Orlicz estimates for the parabolic Schrödinger operator $ L = {\partial _t} - {\Delta _X} + V, $ where the nonnegative potential $ V $ belongs to a reverse Hölder class on nilpotent Lie groups $ {\Bbb G} $ and $ {\Delta _X} $ is the sub-Laplace operator on $ {\Bbb G} $. Under appropriate growth conditions of the Young function, we obtain the regularity estimates of the operator $ L $ in the Orlicz space by using the domain decomposition method. Our results generalize some existing ones of the $ L^{p} $ estimates.

Keywords

• nilpotent lie group
• orlicz space
• parabolic schrödinger operator
• non-negative potential
• domain decomposition method