Michael Lacey

activity

20072024

most citedMultiparameter Riesz Commutators

29 citations · 46 across the 10 of their papers we have counts for

collaborators

11 papers

math.CA2024

Schatten classes and commutators in the two weight setting, II. Riesz transforms

Michael Lacey, Ji Li, Brett D. Wick +1

We characterize the Schatten class $S^{p}$ of the commutator of Riesz transforms $[b, R_{j}]$ in $R^{n}$ ( $j = 1, \dots, n$ ) in the two weight setting for $n < p < \infty$ , by introduc…

math.FA2024

Schatten--Lorentz characterization of Riesz transform commutator associated with Bessel operators

Zhijie Fan, Michael Lacey, Ji Li +1

Let $Δ_{λ}$ be the Bessel operator on the upper half space $R_{+}^{n + 1}$ with $n \geq 0$ and $λ > 0$ , and $R_{λ, j}$ be the $j -$ th Bessel Riesz transform, $j = 1, \dots, n + 1$ . We dem…

math.FA2023

Schatten Class Estimates for Paraproducts in Multi-parameter setting and applications

Michael T. Lacey, Ji Li, Brett D. Wick

Let $Π_{b}$ be a bounded $n$ parameter paraproduct with symbol $b$ . We demonstrate that this operator is in the Schatten class $S^{p}$ , $0 < p < \infty$ , if the symbol is in the $n$ par…

math.FA2022

Besov Space, Schatten Classes And Commutators Of Riesz Transforms Associated With The Neumann Laplacian

Zhijie Fan, Michael Lacey, Ji Li +2

This article provides a deeper study of the Riesz transform commutators associated with the Neumann Laplacian operator $Δ_{N}$ on $R^{n}$ . Along the line of singular value esti…

math.CA2022

Compactness of the Bloom sparse operators and applications

Peng Chen, Michael Lacey, Ji Li +1

We establish the characterization of compactness for the sparse operator (associated with symbol in weighted VMO space) in the two weight setting on the spaces of homogeneous type…

math.FA2022

Schatten classes and commutator in the two weight setting, I. Hilbert transform

Michael Lacey, Ji Li, Brett D. Wick

We characterize the Hilbert--Schmidt class membership of commutator with the Hilbert transform in the two weight setting. The characterization depends upon the symbol of the commut…

math.FA2021

Schatten classes and commutators of Riesz transform on Heisenberg group and applications

Zhijie Fan, Michael Lacey, Ji Li

We study commutators with the Riesz transforms on the Heisenberg group. The Schatten norm of these commutators is characterized in terms of Besov norms of the symbol. This generali…

math.CA2018★ 4 cited

Endpoint sparse bounds for Walsh-Fourier multipliers of Marcinkiewicz type

Wei Chen, Amalia Culiuc, Francesco Di Plinio +2

We prove endpoint-type sparse bounds for Walsh-Fourier Marcinkiewicz multipliers and Littlewood-Paley square functions. These results are motivated by conjectures of Lerner in the…

math.CA2010★ 12 cited

Multi-Parameter Div-Curl Lemmas

Michael T. Lacey, Stefanie Petermichl, Jill C. Pipher +1

We study the possible analogous of the Div-Curl Lemma in classical harmonic analysis and partial differential equations, but from the point of view of the multi-parameter setting.…

math.CA2008★ 1 cited

Composition of Haar Paraproducts: The Random Case

Dmitriy Bilyk, Michael Lacey, Xiaochun Li +1

When is the composition of paraproducts bounded? This is an important, and difficult question, related to to a question of Sarason on composition of Hankel matrices, and the two-we…

math.CA2007★ 29 cited

Multiparameter Riesz Commutators

Michael Lacey, Stefanie Petermichl, Jill Pipher +1

It is shown that product BMO of Chang and Fefferman, defined on the product of Euclidean spaces can be characterized by the multiparameter commutators of Riesz transforms. This ext…