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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Detalles Bibliográficos
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
Descripción
Sumario: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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