English

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 Lp(M)L^p(M) for all p>2p > 2. This extends recent results for Vicsek manifolds, and in particular shows that fractal structure is not necessary for this property.

Keywords

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