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

Abstract

We study multi-parameter Carnot-Carathéodory 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-Carathéodory balls.