New Riemannian manifolds with $L^p$-unbounded Riesz transform for $p > 2$
Classical Analysis and ODEs
2019-10-30 v3 Differential Geometry
Functional Analysis
Abstract
We construct a large class of Riemannian manifolds of arbitrary dimension with Riesz transform unbounded on for all . This extends recent results for Vicsek manifolds, and in particular shows that fractal structure is not necessary for this property.
Cite
@article{arxiv.1707.09781,
title = {New Riemannian manifolds with $L^p$-unbounded Riesz transform for $p > 2$},
author = {Alex Amenta},
journal= {arXiv preprint arXiv:1707.09781},
year = {2019}
}
Comments
Minor corrections and clarifications