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We construct a large class of Riemannian manifolds of arbitrary dimensionwith Riesz transform unbounded on $L^p(M)$ for all $p > 2$. This extends recentresults for Vicsek manifolds, and in particular shows that fractal structure isnot necessary for this property.

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