Multi-parameter Carnot-Caratheodory balls and the theorem of Frobenius

TL;DR

This paper extends the theory of Carnot-Caratheodory balls to multiple parameters, providing a uniform Frobenius theorem and analyzing related maximal functions, advancing geometric control theory.

Contribution

It generalizes single-parameter results to multi-parameter settings and introduces a uniform Frobenius theorem for Carnot-Caratheodory structures.

Findings

Established a uniform version of the Frobenius theorem for multi-parameter Carnot-Caratheodory balls.

Analyzed maximal functions associated with multi-parameter Carnot-Caratheodory balls.

Extended classical results of Nagel, Stein, and Wainger to a multi-parameter context.

Abstract

We study multi-parameter Carnot-Caratheodory balls, generalizing results due to Nagel, Stein, and Wainger in the single parameter setting. The main technical result is seen as a uniform version of the theorem of Frobenius. In addition, we study maximal functions associated to certain multi-parameter families of Carnot-Caratheodory balls.