Unboundedness of potential dependent Riesz transforms for totally irregular measures

We prove that, for totally irregular measures ? on R d with ? 3 , the ( ? 1 ) -dimensional Riesz transform T A V f x = ? ? E y adapted to Schrödinger operator L div + fundamental solution is not bounded 2 . This generalises recent results obtained by Conde-Alonso, Mourgoglou and Tolsa free-space elliptic operators Hölder continuous coefficients since it allows presence of potentials in reverse class H achieve this obtaining new exponential decay estimates kernel as well regularity at local scales determined potential's critical radius function.