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

Department of Mathematics

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

1 Scopus citations

Abstract

This paper provides a weak factorization for the Meyer-type Hardy space H_b¹ (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 CΓ , respectively. Here b(x) = 1 + iA⁰(x) where A⁰ ∈ L^∞(R), and the Cauchy integral CΓ 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
State	Published - 2020

Keywords

BMO
Cauchy integral
Commutator
Hardy space H
VMO
Weak factorization

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abstract = "This paper provides a weak factorization for the Meyer-type Hardy space Hb1 (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 + iA0(x) where A0 ∈ L∞(R), and the Cauchy integral CΓ is associated to the Lipschitz curve Γ = \{x + iA(x): x ∈ R\}.",

keywords = "BMO, Cauchy integral, Commutator, Hardy space H, VMO, Weak factorization",

author = "Yongsheng Han and Ji Li and Cristina Pereyra and Wick, \{Brett D.\}",

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journal = "Studia Mathematica",

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AU - Han, Yongsheng

AU - Li, Ji

AU - Pereyra, Cristina

AU - Wick, Brett D.

N1 - Publisher Copyright: © Instytut Matematyczny PAN, 2020.

PY - 2020

Y1 - 2020

N2 - This paper provides a weak factorization for the Meyer-type Hardy space Hb1 (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 + iA0(x) where A0 ∈ 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 Hb1 (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 + iA0(x) where A0 ∈ L∞(R), and the Cauchy integral CΓ is associated to the Lipschitz curve Γ = {x + iA(x): x ∈ R}.

KW - BMO

KW - Cauchy integral

KW - Commutator

KW - Hardy space H

KW - VMO

KW - Weak factorization

UR - https://www.scopus.com/pages/publications/85092759684

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DO - 10.4064/sm190209-12-8

M3 - Article

AN - SCOPUS:85092759684

SN - 0039-3223

VL - 253

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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Keywords

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