Unboundedness of potential dependent Riesz transforms for totally irregular measures

Julian Bailey, Andrew J. Morris, Maria Carmen Reguera

We prove that, for totally irregular measures $\mu$ on ${\mathbb{R}}^d$ with $d\ge 3$, the $(d-1)$-dimensional Riesz transform $$ T_{A,μ}^{V}f(x) = \int_{\mathbb{R}^d} \nabla_{1}\mat…