BMO estimates for nonvariational operators with discontinuous coefficients structured on Hormander's vector fields on Carnot groups

TL;DR

This paper establishes local BMO estimates for a class of nonvariational operators with discontinuous coefficients structured on Hormander's vector fields within Carnot groups, improving upon existing results even in elliptic cases.

Contribution

It introduces new local BMO estimates for nonvariational operators with discontinuous coefficients on Carnot groups, extending the theory to less regular coefficient classes.

Findings

Established local BMO estimates for operators with discontinuous coefficients

Extended known results to the case of nonvariational operators on Carnot groups

Improved estimates even in the uniformly elliptic case

Abstract

We consider a class of nonvariational linear operators formed by homogeneous left invariant Hormander's vector fields with respect to a structure of Carnot group. The bounded coefficients of the operators belong to "vanishing logarithmic mean oscillation" class with respect to the distance induced by the vector fields (in particular they can be discontinuous). We prove local estimates in "local BMO" spaces intersected with the Lebesgue spaces. Even in the uniformly elliptic case our estimates improve the known results.