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.
Original language | English |
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Pages (from-to) | 4797-4803 |
Number of pages | 7 |
Journal | American Mathematical Society. Proceedings |
Volume | 147 |
Issue number | 11 |
DOIs | |
Publication status | Published - 2019 |
Bibliographical note
Accepted author manuscriptKeywords
- Brownian motion
- Riemannian manifolds
- Riesz transform