Print Email Facebook Twitter A Dichotomy Concerning Uniform Boundedness of Riesz Transforms on Riemannian Manifolds Title A Dichotomy Concerning Uniform Boundedness of Riesz Transforms on Riemannian Manifolds Author Amenta, Alex (TU Delft Analysis) Tolomeo, Leonardo (University of Edinburgh) Date 2019 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. Subject Brownian motionRiemannian manifoldsRiesz transform To reference this document use: http://resolver.tudelft.nl/uuid:db7e6c34-73dc-49bf-bd9d-6a25cbe39353 DOI https://doi.org/10.1090/proc/14730 ISSN 0002-9939 Source American Mathematical Society. Proceedings, 147 (11), 4797-4803 Bibliographical note Accepted author manuscript Part of collection Institutional Repository Document type journal article Rights © 2019 Alex Amenta, Leonardo Tolomeo Files PDF riesz_failure.pdf 418.24 KB Close viewer /islandora/object/uuid:db7e6c34-73dc-49bf-bd9d-6a25cbe39353/datastream/OBJ/view