Some remarks about Poincaré type inequalities and representation formulas in metric spaces of homogeneous type
The authors derive an integral representation formula for a function in terms of its vector field gradient, assuming a less restrictive growth condition on the volumes of balls than was previously known. The authors give the explicit form of the constants involved in the formula. They also show that the required growth condition is satisfied by a large class of Carnot-Carathéodory vector fields.
scientific article; zbMATH DE number 1300152