Julian Bailey

activity

20162021

most citedQuadratic sparse domination and Weighted Estimates for non-integral Square Functions

7 citations · 12 across the 6 of their papers we have counts for

collaborators

6 papers

math.AP2021

Vertical and horizontal Square Functions on a Class of Non-Doubling Manifolds

Julian Bailey, Adam Sikora

We consider a class of non-doubling manifolds $M$ that are the connected sum of a finite number of $N$ -dimensional manifolds of the form $\mathbb{R}^{n_{i}} \times \mathc…

math.CA2020★ 7 cited

Quadratic sparse domination and Weighted Estimates for non-integral Square Functions

Julian Bailey, Gianmarco Brocchi, Maria Carmen Reguera

We prove a quadratic sparse domination result for general non-integral square functions $S$ . That is, we prove an estimate of the form \begin{equation*} \int_{M} (S f)^{2} g \, \ma…

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…

math.FA2018★ 5 cited

The Kato Square Root Problem for Divergence Form Operators with Potential

Julian Bailey

The Kato square root problem for divergence form elliptic operators with potential $V : R^{n} \to C$ is the equivalence statement $\left\Vert (L + V)^{\fr…

math.FA2016

A Hardy-Littlewood Maximal Operator Adapted to the Harmonic Oscillator

Julian Bailey

This paper constructs a Hardy-Littlewood type maximal operator adapted to the Schrödinger operator $L := - Δ + ∣ x ∣^{2}$ acting on $L^{2} (R^{d})$ . It achieves this…