Hardy spaces of exact forms on Lipschitz domains in ℝn

Zengjian Lou; Alan McIntosh

doi:10.1512/iumj.2004.53.2395

Hardy spaces of exact forms on Lipschitz domains in ℝⁿ

Zengjian Lou^*, Alan McIntosh

^*Corresponding author for this work

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

10 Citations (Scopus)

Abstract

We introduce Hardy spaces ℋ_z,d¹(Ω, Λ^ℓ) of exact ℓ-forms on domains Ω in ℝ^N. We prove atomic decompositions of ℋ_z,d ¹(Ω, Λ^ℓ) when Ω is a special Lipschitz domain or a bounded strongly Lipschitz domain in ℝ^N and use these atomic decompositions to characterize dual spaces of ℋ_z,d¹(Ω, Λ^ℓ). We also establish a "div-curl" type theorem on Ω with an application to coercivity.

Original language	English
Pages (from-to)	583-611
Number of pages	29
Journal	Indiana University Mathematics Journal
Volume	53
Issue number	2
DOIs	https://doi.org/10.1512/iumj.2004.53.2395
Publication status	Published - 2004

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abstract = "We introduce Hardy spaces ℋz,d1(Ω, Λℓ) of exact ℓ-forms on domains Ω in ℝN. We prove atomic decompositions of ℋz,d 1(Ω, Λℓ) when Ω is a special Lipschitz domain or a bounded strongly Lipschitz domain in ℝN and use these atomic decompositions to characterize dual spaces of ℋz,d1(Ω, Λℓ). We also establish a {"}div-curl{"} type theorem on Ω with an application to coercivity.",

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author = "Zengjian Lou and Alan McIntosh",

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T1 - Hardy spaces of exact forms on Lipschitz domains in ℝn

AU - Lou, Zengjian

AU - McIntosh, Alan

PY - 2004

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N2 - We introduce Hardy spaces ℋz,d1(Ω, Λℓ) of exact ℓ-forms on domains Ω in ℝN. We prove atomic decompositions of ℋz,d 1(Ω, Λℓ) when Ω is a special Lipschitz domain or a bounded strongly Lipschitz domain in ℝN and use these atomic decompositions to characterize dual spaces of ℋz,d1(Ω, Λℓ). We also establish a "div-curl" type theorem on Ω with an application to coercivity.

AB - We introduce Hardy spaces ℋz,d1(Ω, Λℓ) of exact ℓ-forms on domains Ω in ℝN. We prove atomic decompositions of ℋz,d 1(Ω, Λℓ) when Ω is a special Lipschitz domain or a bounded strongly Lipschitz domain in ℝN and use these atomic decompositions to characterize dual spaces of ℋz,d1(Ω, Λℓ). We also establish a "div-curl" type theorem on Ω with an application to coercivity.

KW - Atomic decomposition

KW - BMO

KW - Coercivity

KW - Div-curl

KW - Hardy spaces of exact forms

KW - Lipschitz domain

UR - https://www.scopus.com/pages/publications/3042541250

U2 - 10.1512/iumj.2004.53.2395

DO - 10.1512/iumj.2004.53.2395

M3 - Article

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VL - 53

SP - 583

EP - 611

JO - Indiana University Mathematics Journal

JF - Indiana University Mathematics Journal

IS - 2

ER -

Hardy spaces of exact forms on Lipschitz domains in ℝⁿ

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