Julian Bailey

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20182021

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math.CA2020

Weights of Exponential Growth and Decay for Schrödinger-type operators

Julian Bailey

Fix $d \geq 3$ and $1 < p < \infty$ . Let $V : R^{d} \to [0, \infty)$ belong to the reverse Hölder class $R H_{d /2}$ and consider the Schrödinger operator $L_{V} := -…

math.CA2020

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 $μ$ on $R^{d}$ with $d \geq 3$ , the $(d - 1)$ -dimensional Riesz transform $$ T_{A,μ}^{V}f(x) = \int_{\mathbb{R}^d} \nabla_{1}\mat…