Some remarks about Poincaré type inequalities and representation formulas in metric spaces of homogeneous type

Journal of Inequalities and Applications

关键词: Poincaré;    inequality;    Representation formulas;    Carnot–;    Carathé;    odory metrics;    Riemannian manifolds;   

DOI  :  

来源: DOAJ

【 摘 要 】

We 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. We give the explicit form of the constants involved in the formula. We also show that the required growth condition is satisfied by a large class of Carnot– Carathéodory vector fields.

【 授权许可】

Unknown