A note on weak factorization of a Meyer-type Hardy space via a Cauchy integral operator

Yongsheng Han; Ji Li; Cristina Pereyra; Brett D. Wick

doi:10.4064/sm190209-12-8

A note on weak factorization of a Meyer-type Hardy space via a Cauchy integral operator

Yongsheng Han, Ji Li, Cristina Pereyra, Brett D. Wick

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

Abstract

This paper provides a weak factorization for the Meyer-type Hardy space H¹_b(R), and characterizations of its dual BMO_b(R) and its predual VMO_b(R) via boundedness and compactness of a suitable commutator with the Cauchy integral C_Γ, respectively. Here b(x)=1+iA′(x) where A′∈L^∞(R), and the Cauchy integral C_Γ is associated to the Lipschitz curve Γ={x+iA(x):x∈R}.

Original language	English
Pages (from-to)	307-327
Number of pages	21
Journal	Studia Mathematica
Volume	253
Issue number	3
DOIs	https://doi.org/10.4064/sm190209-12-8
Publication status	Published - 2020

Keywords

Cauchy integral
commutator
wark factorization
Hardy space H¹
BMO
VMO
Commutator
Weak factorization
Hardy space H

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abstract = "This paper provides a weak factorization for the Meyer-type Hardy space H1b(R), and characterizations of its dual BMOb(R) and its predual VMOb(R) via boundedness and compactness of a suitable commutator with the Cauchy integral CΓ, respectively. Here b(x)=1+iA′(x) where A′∈L∞(R), and the Cauchy integral CΓ is associated to the Lipschitz curve Γ={x+iA(x):x∈R}.",

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AU - Li, Ji

AU - Pereyra, Cristina

AU - Wick, Brett D.

PY - 2020

Y1 - 2020

N2 - This paper provides a weak factorization for the Meyer-type Hardy space H1b(R), and characterizations of its dual BMOb(R) and its predual VMOb(R) via boundedness and compactness of a suitable commutator with the Cauchy integral CΓ, respectively. Here b(x)=1+iA′(x) where A′∈L∞(R), and the Cauchy integral CΓ is associated to the Lipschitz curve Γ={x+iA(x):x∈R}.

AB - This paper provides a weak factorization for the Meyer-type Hardy space H1b(R), and characterizations of its dual BMOb(R) and its predual VMOb(R) via boundedness and compactness of a suitable commutator with the Cauchy integral CΓ, respectively. Here b(x)=1+iA′(x) where A′∈L∞(R), and the Cauchy integral CΓ is associated to the Lipschitz curve Γ={x+iA(x):x∈R}.

KW - Cauchy integral

KW - commutator

KW - wark factorization

KW - Hardy space H¹

KW - BMO

KW - VMO

KW - Commutator

KW - Weak factorization

KW - Hardy space H

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SP - 307

EP - 327

JO - Studia Mathematica

JF - Studia Mathematica

IS - 3

ER -

A note on weak factorization of a Meyer-type Hardy space via a Cauchy integral operator

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