Commutators of Cauchy-Szego type integrals for domains in C^n with minimal smoothness

DOI10.1512/iumj.2021.70.8573zbMath1476.30141arXiv1809.08335OpenAlexW3196476880WikidataQ114053250 ScholiaQ114053250MaRDI QIDQ3380489

Xuan Thinh Duong, Brett D. Wick, Ji Li, Michael T. Lacey, Qing Yan Wu

Publication date: 29 September 2021

Published in: Indiana University Mathematics Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.08335

zbMATH Keywords

BMO spacecommutatorCauchy-type integralsVMO spacedomains in \(\mathbb{C}^n\)

Mathematics Subject Classification ID

Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Function spaces arising in harmonic analysis (42B35) Integral representations; canonical kernels (Szeg?, Bergman, etc.) (32A25) Singular integrals of functions in several complex variables (32A55) Harmonic analysis of several complex variables (32A50)

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Cites Work

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• The Cauchy integral in \(\mathbb{C}^n\) for domains with minimal smoothness
• The Cauchy-Szegő projection for domains in \(\mathbb{C}^n\) with minimal smoothness
• Commutators in the two-weight setting
• On bounded bilinear forms
• Estimates for the Bergman and Szegö kernels in \({\mathbb{C}}^ 2\)
• Geometric Lipschitz spaces and applications to complex function theory and nilpotent groups
• Factorization theorems for Hardy spaces in several variables
• On the compactness of operators of Hankel type
• Lower bound of Riesz transform kernels and commutator theorems on stratified nilpotent Lie groups
• The Bergman kernel and biholomorphic mappings of pseudoconvex domains
• Endpoint estimates for commutators of singular integral operators
• Compensated compactness and Hardy spaces
• Sparse and weighted estimates for generalized Hörmander operators and commutators
• On pointwise and weighted estimates for commutators of Calderón-Zygmund operators
• Two weight commutators in the Dirichlet and Neumann Laplacian settings
• The unified theory for the necessity of bounded commutators and applications
• Two weight commutators on spaces of homogeneous type and applications
• A Commutator Theorem and Weighted BMO
• Commutators of singular integrals revisited
• The Cauchy integral, bounded and compact commutators
• The Cauchy-Leray integral: counter-examples to the L^p-theory
• Factorization for Hardy spaces and characterization for BMO spaces via commutators in the Bessel setting
• Boundedness and compactness characterizations of Cauchy integral commutators on Morrey spaces
• Boundary Behavior of Holomorphic Functions of Several Complex Variables. (MN-11)
• Boundedness and compactness of integral operators on spaces of homogeneous type and applications. I
• Boundedness and compactness of integral operators on spaces of homogeneous type and applications. II