Bourgain-Brezis Estimates on Symmetric Spaces of Non-compact Type
Analysis of PDEs
2017-07-04 v2 Classical Analysis and ODEs
Differential Geometry
Abstract
Let M be a globally Riemannian symmetric space. We prove a duality estimate between pairings of vector fields with divergence zero and and in L^1 with vector fields in a critical Sobolev space on M. As a consequence we get a sharp Calderon-Zygmund estimate for solutions to Poisson's equation on M, where the right side data is manufactured from divergence free vector fields which are in L^1. Such a result was proved earlier by Jean Bourgain and Haim Brezis on Euclidean space.
Keywords
Cite
@article{arxiv.1610.00503,
title = {Bourgain-Brezis Estimates on Symmetric Spaces of Non-compact Type},
author = {Sagun Chanillo and Jean Van Schaftingen and Po-lam Yung},
journal= {arXiv preprint arXiv:1610.00503},
year = {2017}
}
Comments
Final version of the paper to appear in J. Functional Analysis