Poincare inequalities, isoperimetric estimates, and representation formulas on product spaces
Poincare inequalities, isoperimetric estimates, and representation formulas on product spaces
We derive Sobolev-Poincaré inequalities for product balls in case the component spaces are metric spaces associated with appropriate collections of vector fields on Euclidean space.We also consider weighted versions of such inequalities, representation formulas which express a function in terms of integrals of potential type of its component vector field …