Tame algebra estimates for product and flag kernels on graded Lie groups

TL;DR

This paper establishes tame algebra estimates for product and flag kernels on graded Lie groups, providing a new Banach-algebraic proof of their inversion theorem, which is important for nonlinear PDE analysis.

Contribution

It introduces tame algebra estimates for these kernels on graded Lie groups and offers a novel Banach-algebraic proof of their inversion theorem.

Findings

Proved tame algebra estimates for product and flag kernels.

Derived a new Banach-algebraic inversion theorem.

Enhanced tools for nonlinear PDE analysis on graded Lie groups.

Abstract

We prove that product kernels and flag kernels on a direct product of graded Lie groups $G_1 \times \cdots \times G_{\nu}$ satisfy so-called \emph{tame algebra estimates}. Tame algebra estimates are central to the study of nonlinear partial differential equations via, for instance, the Nash-Moser inverse function theorem. In addition, the special structure of these estimates generates a new Banach-algebraic proof of an inversion theorem for product kernels and flag kernels.