The molecular characterization of weighted Hardy spaces

Ming Yi Lee; Chin Cheng Lin

doi:10.1006/jfan.2001.3839

The molecular characterization of weighted Hardy spaces

Ming Yi Lee, Chin Cheng Lin

Department of Mathematics

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

40 Scopus citations

Abstract

We first define molecules for weighted Hardy spaces and prove their molecular characters. As an application, we give sufficient conditions on the kernel k such that the convolution operator T f = k * f is bounded on weighted Hardy spaces H_w^p(ℝⁿ), w ∈ A₁. We also get the H_w^p(ℝ), 1/2 <p ≤ 1, boundedness of the Hilbert transform and the H_w^p(ℝⁿ), n/(n+1) < p ≤ 1, boundedness of the Riesz transforms.

Original language	English
Pages (from-to)	442-460
Number of pages	19
Journal	Journal of Functional Analysis
Volume	188
Issue number	2
DOIs	https://doi.org/10.1006/jfan.2001.3839
State	Published - 1 Feb 2002

Keywords

Atomic decomposition
Hilbert transform
Molecular character
Riesz transforms
Singular integrals
Weighted Hardy spaces

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10.1006/jfan.2001.3839

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abstract = "We first define molecules for weighted Hardy spaces and prove their molecular characters. As an application, we give sufficient conditions on the kernel k such that the convolution operator T f = k * f is bounded on weighted Hardy spaces Hwp(ℝn), w ∈ A1. We also get the Hwp(ℝ), 1/2 wp(ℝn), n/(n+1) < p ≤ 1, boundedness of the Riesz transforms.",

keywords = "Atomic decomposition, Hilbert transform, Molecular character, Riesz transforms, Singular integrals, Weighted Hardy spaces",

author = "Lee, {Ming Yi} and Lin, {Chin Cheng}",

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AU - Lee, Ming Yi

AU - Lin, Chin Cheng

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Y1 - 2002/2/1

N2 - We first define molecules for weighted Hardy spaces and prove their molecular characters. As an application, we give sufficient conditions on the kernel k such that the convolution operator T f = k * f is bounded on weighted Hardy spaces Hwp(ℝn), w ∈ A1. We also get the Hwp(ℝ), 1/2 wp(ℝn), n/(n+1) < p ≤ 1, boundedness of the Riesz transforms.

AB - We first define molecules for weighted Hardy spaces and prove their molecular characters. As an application, we give sufficient conditions on the kernel k such that the convolution operator T f = k * f is bounded on weighted Hardy spaces Hwp(ℝn), w ∈ A1. We also get the Hwp(ℝ), 1/2 wp(ℝn), n/(n+1) < p ≤ 1, boundedness of the Riesz transforms.

KW - Atomic decomposition

KW - Hilbert transform

KW - Molecular character

KW - Riesz transforms

KW - Singular integrals

KW - Weighted Hardy spaces

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EP - 460

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 2

ER -

The molecular characterization of weighted Hardy spaces

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Keywords

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