An approximation theorem for Hardy functions on $\mathbb {C}$-linearly convex domains of infinite type in $\mathbb {C}^2$

DOI10.4064/cm7807-5-2019zbMath1452.32017OpenAlexW3013597364MaRDI QIDQ5126663

Ly Kim Ha

Publication date: 20 October 2020

Published in: Colloquium Mathematicum (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4064/cm7807-5-2019

zbMATH Keywords

approximationHardy spacesCauchy-Fantappiè forms\(\mathbb{C}\)-linearly convex domains

Mathematics Subject Classification ID

Integral representations, constructed kernels (e.g., Cauchy, Fantappiè-type kernels) (32A26) (H^p)-spaces, Nevanlinna spaces of functions in several complex variables (32A35) Geometric convexity in several complex variables (32F99)

Cites Work

• The Caratheodory metric and holomorphic maps on a class of weakly pseudoconvex domains
• Hölder and \(L^ p\) estimates for \({\bar \partial}_ b\) on weakly pseudo-convex boundaries in \({\mathbb C}^ 2\)
• The Cauchy transform and Henkin operator on convex domains of maximal type \(F\) in \(\mathbb{C}^2\)
• Tangential Cauchy-Riemann equations on pseudoconvex boundaries of finite and infinite type in \(\mathbb {C}^2\)
• Cauchy-type integrals in several complex variables
• L^∞-continuity of Henkin operators solving in certain weakly pseudoconvex domains of ℂ²
• H p -Functions on Strictly Pseudoconvex Domains
• Real Analytic Boundary Regularity of the Cauchy Kernel on Convex Domains
• Several Complex Variables and Banach Algebras
• -APPROXIMATION OF HOLOMORPHIC FUNCTIONS ON A CLASS OF CONVEX DOMAINS
• INTEGRAL REPRESENTATIONS OF FUNCTIONS HOLOMORPHIC IN STRICTLY PSEUDO-CONVEX DOMAINS AND SOME APPLICATIONS
• Boundary Behavior of Holomorphic Functions of Several Complex Variables. (MN-11)
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