A parabolic version of Corona decompositions

Abstract

Let $E$ be a subset in $(n+1)$-dimensional Euclidian space with parabolic homogeneity, codimension $1$, and with an appropriate surface measure $\sigma$ associated to it. We define a parabolic version of Corona decomposition of $E$ and establish two results on sufficient conditions for the existence of parabolic Corona decomposition for $E$. Both results are parabolic versions of well-known results due to G. David and S. Semmes.