ZYGMUND DILATIONS: BILINEAR ANALYSIS AND COMMUTATOR ESTIMATES

Emil Airta; Kangwei Li; Henri Martikainen

doi:10.1090/tran/9366

ZYGMUND DILATIONS: BILINEAR ANALYSIS AND COMMUTATOR ESTIMATES

Emil Airta
, Kangwei Li
, Henri Martikainen

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We develop both bilinear theory and commutator estimates in the context of entangled dilations, specifically Zygmund dilations (x₁, x₂, x₃) →⃓ (δ₁x₁, δ₂x₂, δ₁δ₂x₃) in R³. We construct bilinear versions of recent dyadic multiresolution methods for Zygmund dilations and apply them to prove a paraproduct free T1 theorem for bilinear singular integrals invariant under Zygmund dilations. Independently, we prove linear commutator estimates even when the underlying singular integrals do not satisfy weighted estimates with Zygmund weights. This requires new paraproduct estimates.

Original language	English
Pages (from-to)	4581-4625
Number of pages	45
Journal	Transactions of the American Mathematical Society
Volume	378
Issue number	7
DOIs	https://doi.org/10.1090/tran/9366
State	Published - Jul 2025

Keywords

Singular integrals
Zygmund dilations
multi-parameter analysis
multiresolution analysis
weighted estimates

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10.1090/tran/9366

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title = "ZYGMUND DILATIONS: BILINEAR ANALYSIS AND COMMUTATOR ESTIMATES",

abstract = "We develop both bilinear theory and commutator estimates in the context of entangled dilations, specifically Zygmund dilations (x1, x2, x3) →⃓ (δ1x1, δ2x2, δ1δ2x3) in R3. We construct bilinear versions of recent dyadic multiresolution methods for Zygmund dilations and apply them to prove a paraproduct free T1 theorem for bilinear singular integrals invariant under Zygmund dilations. Independently, we prove linear commutator estimates even when the underlying singular integrals do not satisfy weighted estimates with Zygmund weights. This requires new paraproduct estimates.",

keywords = "Singular integrals, Zygmund dilations, multi-parameter analysis, multiresolution analysis, weighted estimates",

author = "Emil Airta and Kangwei Li and Henri Martikainen",

note = "Publisher Copyright: {\textcopyright}2025 American Mathematical Society.",

year = "2025",

month = jul,

doi = "10.1090/tran/9366",

language = "English",

volume = "378",

pages = "4581--4625",

journal = "Transactions of the American Mathematical Society",

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TY - JOUR

T1 - ZYGMUND DILATIONS

T2 - BILINEAR ANALYSIS AND COMMUTATOR ESTIMATES

AU - Airta, Emil

AU - Li, Kangwei

AU - Martikainen, Henri

PY - 2025/7

Y1 - 2025/7

N2 - We develop both bilinear theory and commutator estimates in the context of entangled dilations, specifically Zygmund dilations (x1, x2, x3) →⃓ (δ1x1, δ2x2, δ1δ2x3) in R3. We construct bilinear versions of recent dyadic multiresolution methods for Zygmund dilations and apply them to prove a paraproduct free T1 theorem for bilinear singular integrals invariant under Zygmund dilations. Independently, we prove linear commutator estimates even when the underlying singular integrals do not satisfy weighted estimates with Zygmund weights. This requires new paraproduct estimates.

AB - We develop both bilinear theory and commutator estimates in the context of entangled dilations, specifically Zygmund dilations (x1, x2, x3) →⃓ (δ1x1, δ2x2, δ1δ2x3) in R3. We construct bilinear versions of recent dyadic multiresolution methods for Zygmund dilations and apply them to prove a paraproduct free T1 theorem for bilinear singular integrals invariant under Zygmund dilations. Independently, we prove linear commutator estimates even when the underlying singular integrals do not satisfy weighted estimates with Zygmund weights. This requires new paraproduct estimates.

KW - Singular integrals

KW - Zygmund dilations

KW - multi-parameter analysis

KW - multiresolution analysis

KW - weighted estimates

UR - https://www.scopus.com/pages/publications/105008550905

U2 - 10.1090/tran/9366

DO - 10.1090/tran/9366

M3 - Article

AN - SCOPUS:105008550905

SN - 0002-9947

VL - 378

SP - 4581

EP - 4625

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 7

ER -

ZYGMUND DILATIONS: BILINEAR ANALYSIS AND COMMUTATOR ESTIMATES

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