Commutators of Singular Integral Operators Satisfying a Variant of a Lipschitz Condition

Let T be a singular integral operator with its kernel satisfying |K(x − y) − ∑(k=1) (ℓ)‍B (k)(x)ϕ (k)(y)| ≤ C | y|(γ)/|x − y|(n+γ), |x | > 2 | y | > 0, where B (k) and ϕ (k)  (k = 1,…, ℓ) are appropriate functions and γ and C are positive constants. For [Formula: see text] with b (j) ∈ BMO(ℝ(n...

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Autores principales: Zhang, Pu, Zhang, Daiqing
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2014
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4032734/
https://www.ncbi.nlm.nih.gov/pubmed/24892067
http://dx.doi.org/10.1155/2014/641705
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author Zhang, Pu
Zhang, Daiqing
author_facet Zhang, Pu
Zhang, Daiqing
author_sort Zhang, Pu
collection PubMed
description Let T be a singular integral operator with its kernel satisfying |K(x − y) − ∑(k=1) (ℓ)‍B (k)(x)ϕ (k)(y)| ≤ C | y|(γ)/|x − y|(n+γ), |x | > 2 | y | > 0, where B (k) and ϕ (k)  (k = 1,…, ℓ) are appropriate functions and γ and C are positive constants. For [Formula: see text] with b (j) ∈ BMO(ℝ(n)), the multilinear commutator [Formula: see text] generated by T and [Formula: see text] is formally defined by [Formula: see text]. In this paper, the weighted L (p)-boundedness and the weighted weak type Llog⁡L estimate for the multilinear commutator [Formula: see text] are established.
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spelling pubmed-40327342014-06-02 Commutators of Singular Integral Operators Satisfying a Variant of a Lipschitz Condition Zhang, Pu Zhang, Daiqing ScientificWorldJournal Research Article Let T be a singular integral operator with its kernel satisfying |K(x − y) − ∑(k=1) (ℓ)‍B (k)(x)ϕ (k)(y)| ≤ C | y|(γ)/|x − y|(n+γ), |x | > 2 | y | > 0, where B (k) and ϕ (k)  (k = 1,…, ℓ) are appropriate functions and γ and C are positive constants. For [Formula: see text] with b (j) ∈ BMO(ℝ(n)), the multilinear commutator [Formula: see text] generated by T and [Formula: see text] is formally defined by [Formula: see text]. In this paper, the weighted L (p)-boundedness and the weighted weak type Llog⁡L estimate for the multilinear commutator [Formula: see text] are established. Hindawi Publishing Corporation 2014 2014-05-04 /pmc/articles/PMC4032734/ /pubmed/24892067 http://dx.doi.org/10.1155/2014/641705 Text en Copyright © 2014 P. Zhang and D. Zhang. https://creativecommons.org/licenses/by/3.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Zhang, Pu
Zhang, Daiqing
Commutators of Singular Integral Operators Satisfying a Variant of a Lipschitz Condition
title Commutators of Singular Integral Operators Satisfying a Variant of a Lipschitz Condition
title_full Commutators of Singular Integral Operators Satisfying a Variant of a Lipschitz Condition
title_fullStr Commutators of Singular Integral Operators Satisfying a Variant of a Lipschitz Condition
title_full_unstemmed Commutators of Singular Integral Operators Satisfying a Variant of a Lipschitz Condition
title_short Commutators of Singular Integral Operators Satisfying a Variant of a Lipschitz Condition
title_sort commutators of singular integral operators satisfying a variant of a lipschitz condition
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4032734/
https://www.ncbi.nlm.nih.gov/pubmed/24892067
http://dx.doi.org/10.1155/2014/641705
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AT zhangdaiqing commutatorsofsingularintegraloperatorssatisfyingavariantofalipschitzcondition

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