A Dichotomy Concerning Uniform Boundedness of Riesz Transforms on Riemannian Manifolds
More Info
expand_more
expand_more
Abstract
Given a sequence of complete Riemannian manifolds (Mn) of the same dimension, we construct a complete Riemannian manifold M such that for all p ∈(1,∞) the Lp-norm of the Riesz transform on M dominates the Lpnorm of the Riesz transform on Mn for all n. Thus we establish the following dichotomy: Given p and d, either there is a uniform Lp bound on the Riesz transform over all complete d-dimensional Riemannian manifolds, or there exists a complete Riemannian manifold with Riesz transform unbounded on Lp.
Files
S0002_9939_2019_14730_4.pdf
(pdf | 0.188 Mb)
Unknown license
Download not available