Michel Alexis

activity

20142023

collaborators

9 papers

math.FA2023

Haar basis testing

Michel Alexis, Jose Luis Luna-Garcia, Eric T. Sawyer

We show that for two doubling measures $σ$ and $ω$ on $R^{n}$ and any fixed dyadic grid $D$ in $R^{n}$ , \[ \mathfrak{N}_{\mathbf{R}^{λ, n}}\left( σ,ω\ri…

math.CA2023

The scalar $T 1$ theorem for pairs of doubling measures fails for Riesz transforms when p not 2

Michel Alexis, José Luis Luna-Garcia, Eric Sawyer +1

We show that for an individual Riesz transform in the setting of doubling measures, the scalar $T 1$ theorem fails when $p \neq = 2$ : for each $p \in (1, \infty) ∖ {2}$ , we…

math.FA2023

The T1 theorem for the Hilbert transform fails when p is not 2

Michel Alexis, Jose Luis Luna-Garcia, Eric T. Sawyer +1

Given p between 1 and infinity, but not 2, we show that the T1 theorem for the Hilbert transform fails for L^{p}, despite holding for p equal to 2

math.CA2022

The Steklov problem and Remainder Estimates for Krein Systems generated by a Muckenhoupt weight

Michel Alexis

We show that solutions to Krein systems, the continuous frequency analogue of orthogonal polynomials on the unit circle, generated by an $A_{2} (R)$ weight $w$ satisfying $w…

math.CA2022

Stability of Weighted Norm Inequalities

Michel Alexis, José Luis Luna Garcia, Eric Sawyer +1

We show that while individual Riesz transforms are two weight norm stable under biLipschitz change of variables on $A_{\infty}$ weights, they are two weight norm unstable under eve…

math.CA2022

Tops of dyadic grids

Michel Alexis, Eric Sawyer, Ignacio Uriarte-Tuero

We extend the notion of a dyadic grid of cubes in Euclidean space to include infinite dyadic cubes. These `tops' of a dyadic grid form a tiling of Euclidean space which is subject…

math.CA2021

A weak to strong type T1 theorem for general smooth Calderón-Zygmund operators with doubling weights, II

Michel Alexis, Eric T. Sawyer, Ignacio Uriarte-Tuero

We consider the weak to strong type problem for two weight norm inequalities for Calderón-Zygmund operators with doubling weights. We show that if a Calderón-Zygmund operator T is…

math.CA2019

Continuity of weighted operators, Muckenhoupt $A_{p}$ weights, and Steklov problem for orthogonal polynomials

Michel Alexis, Alexander Aptekarev, Sergey Denisov

We consider weighted operators acting on $L^{p} (R^{d})$ and show that they depend continuously on the weight $w \in A_{p} (R^{d})$ in the operator topology. Then, we use th…

math.CO2014

Clique-Relaxed Competitive Graph Coloring

Michel Alexis, Davis Shurbert, Charles Dunn +1

We investigate a variation of the graph coloring game, as studied in [2]. In the original coloring game, two players, Alice and Bob, alternate coloring vertices on a graph with leg…

Haar basis testing

The scalar T1 theorem for pairs of doubling measures fails for Riesz transforms when p not 2

The T1 theorem for the Hilbert transform fails when p is not 2

The Steklov problem and Remainder Estimates for Krein Systems generated by a Muckenhoupt weight

Stability of Weighted Norm Inequalities

Tops of dyadic grids

A weak to strong type T1 theorem for general smooth Calderón-Zygmund operators with doubling weights, II

Continuity of weighted operators, Muckenhoupt Ap​ weights, and Steklov problem for orthogonal polynomials

Clique-Relaxed Competitive Graph Coloring

The scalar $T 1$ theorem for pairs of doubling measures fails for Riesz transforms when p not 2

Continuity of weighted operators, Muckenhoupt $A_{p}$ weights, and Steklov problem for orthogonal polynomials