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arXiv · 1610.00503

Bourgain-Brezis Estimates on Symmetric Spaces of Non-compact Type

Sagun Chanillo·Jean Van Schaftingen·Po-lam Yung
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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.

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Sagun Chanillo, Jean Van Schaftingen, Po-lam Yung. 2016-10-03. Bourgain-Brezis Estimates on Symmetric Spaces of Non-compact Type. https://doi.org/10.1016/j.jfa.2017.05.005

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