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arXiv · 1707.09781

New Riemannian manifolds with $L^p$-unbounded Riesz transform for $p > 2$

Alex Amenta
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Abstract

We construct a large class of Riemannian manifolds of arbitrary dimension with Riesz transform unbounded on $L^p(M)$ for all $p > 2$. This extends recent results for Vicsek manifolds, and in particular shows that fractal structure is not necessary for this property.

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Alex Amenta. 2017-07-31. New Riemannian manifolds with $L^p$-unbounded Riesz transform for $p > 2$. https://arxiv.org/abs/1707.09781

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