Michael Frazier

activity

20142020

most citedGlobal estimates for kernels of Neumann series and Green's functions

23 citations · 35 across the 4 of their papers we have counts for

collaborators

5 papers

math.AP2020★ 1 cited

Positive solutions and harmonic measure for Schrödinger operators in uniform domains

Michael W. Frazier, Igor E. Verbitsky

We give bilateral pointwise estimates for positive solutions of the equation \begin{equation*} \left\{ \begin{aligned} -\triangle u & = ωu \, \,& & \mbox{in} \, \, Ω, \quad u \ge 0…

math.CA2019

Littlewood-Paley Theory for Matrix-Weighted Function Spaces

Michael Frazier, Svetlana Roudenko

We define the vector-valued, matrix-weighted function spaces $F ˙_{p}^{α q} (W)$ (homogeneous) and $F_{p}^{α q} (W)$ (inhomogeneous) on $R^{n}$ , for $α \in R$ , $0<p<\inf…

math.AP2018★ 1 cited

Existence of the gauge for fractional Laplacian Schrödinger operators

Michael W. Frazier, Igor E. Verbitsky

Let $Ω \subseteq R^{n}$ be an open set, where $n \geq 2$ . Suppose $ω$ is a locally finite Borel measure on $Ω$ . For $α \in (0, 2)$ , define the fractional Laplacian $(-\triangle…

math.AP2015★ 10 cited

Positive solutions to Schrödinger's equation and the exponential integrability of the balayage

Michael Frazier, Igor Verbitsky

Let $Ω \subset R^{n}$ , for $n \geq 2$ , be a bounded $C^{2}$ domain. Let $q \in L_{l oc}^{1} (Ω)$ with $q \geq 0$ . We give necessary conditions and matching sufficient conditions,…

math.AP2014★ 23 cited

Global estimates for kernels of Neumann series and Green's functions

Michael Frazier, Fedor Nazarov, Igor Verbitsky

We obtain global pointwise estimates for kernels of the resolvents $(I - T)^{- 1}$ of integral operators \[Tf(x) = \int_Ω K(x, y) f(y) d ω(y)\] on $L^{2} (Ω, ω)$ under the assumptions th…