Representation formulas and Fatou-Kato theorems for heat operators on stratified groups

Abstract

In this note, we provide a characterization of non-negative L-caloric functions on strips, where L is a sub-Laplacian on a stratified group. We prove representation results, Fatou-type and uniqueness theorems analogous to the classical Poisson Stieltjes formula and to Kato’s theorem concerning with positive solutions to the heat equation.

Keywords

• carnot groups
• non-negative caloric functions
• fatou and kato theorems
• uniqueness theorems