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

Published 31 Jul 2017 in math.CA, math.DG, and math.FA | (1707.09781v3)

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

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