A new class of weights associated with Schrödinger operator on Heisenberg groups and applications

Abstract

We extend the new class of Euclidean weights constructed by Bongioanni et al. (J Math Anal Appl 373:563–579, 2011) to the setting of Heisenberg groups. Then we show that various well-known operators are bounded on the corresponding new weighted Lebesgue spaces. The process of proving these results produces several interesting estimates of independent interest.