On the atomic decomposition for Hardy spaces on Lipschitz domains of Rn

Xuan Thinh Duong; Lixin Yan

doi:10.1016/j.jfa.2003.10.013

On the atomic decomposition for Hardy spaces on Lipschitz domains of Rn

Xuan Thinh Duong, Lixin Yan^*

^*Corresponding author for this work

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

7 Citations (Scopus)

Abstract

Let Ω be a special Lipschitz domain on ℝⁿ, and L be a second-order elliptic self-adjoint operator in divergence form L=-div(A∇) on Lipschitz domain Ω subject to Neumann boundary condition. In this paper, we give a simple proof of the atomic decomposition for Hardy spaces H_N^p (Ω) of Ω for a range of p, by means of nontangential maximal function associated with the Poisson semigroup of L.

Original language	English
Pages (from-to)	476-486
Number of pages	11
Journal	Journal of Functional Analysis
Volume	215
Issue number	2
DOIs	https://doi.org/10.1016/j.jfa.2003.10.013
Publication status	Published - 15 Oct 2004

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abstract = "Let Ω be a special Lipschitz domain on ℝn, and L be a second-order elliptic self-adjoint operator in divergence form L=-div(A∇) on Lipschitz domain Ω subject to Neumann boundary condition. In this paper, we give a simple proof of the atomic decomposition for Hardy spaces HNp (Ω) of Ω for a range of p, by means of nontangential maximal function associated with the Poisson semigroup of L.",

author = "Duong, {Xuan Thinh} and Lixin Yan",

year = "2004",

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AU - Yan, Lixin

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N2 - Let Ω be a special Lipschitz domain on ℝn, and L be a second-order elliptic self-adjoint operator in divergence form L=-div(A∇) on Lipschitz domain Ω subject to Neumann boundary condition. In this paper, we give a simple proof of the atomic decomposition for Hardy spaces HNp (Ω) of Ω for a range of p, by means of nontangential maximal function associated with the Poisson semigroup of L.

AB - Let Ω be a special Lipschitz domain on ℝn, and L be a second-order elliptic self-adjoint operator in divergence form L=-div(A∇) on Lipschitz domain Ω subject to Neumann boundary condition. In this paper, we give a simple proof of the atomic decomposition for Hardy spaces HNp (Ω) of Ω for a range of p, by means of nontangential maximal function associated with the Poisson semigroup of L.

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DO - 10.1016/j.jfa.2003.10.013

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JO - Journal of Functional Analysis

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On the atomic decomposition for Hardy spaces on Lipschitz domains of Rn

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