Franchi, Bruno; Wheeden, Richard L. Some remarks about Poincaré type inequalities and representation formulas in metric spaces of homogeneous type. (English) Zbl 0934.46037 J. Inequal. Appl. 3, No. 1, 65-89 (1999). 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. Reviewer: S.Wedrychowicz (Rzeszów) Cited in 4 Documents MSC: 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems Keywords:integral representation; vector field gradient; growth condition; Carnot-Carathéodory vector fields PDFBibTeX XMLCite \textit{B. Franchi} and \textit{R. L. Wheeden}, J. Inequal. Appl. 3, No. 1, 65--89 (1999; Zbl 0934.46037) Full Text: DOI EuDML