Extension and restriction of holomorphic functions on convex finite type domains

zbMath1233.32005MaRDI QIDQ648754

Michał Jasiczak

Publication date: 28 November 2011

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.ijm/1318598671

zbMATH Keywords

Bergman space\(p\)-integrable holomorphic functionconvex domain of finite typefinite positive Borel measurenon-isotropic polydiskWhitney type cover

Mathematics Subject Classification ID

(H^p)-spaces, Nevanlinna spaces of functions in several complex variables (32A35) Bergman spaces of functions in several complex variables (32A36) Finite-type domains (32T25) Analytical consequences of geometric convexity (vanishing theorems, etc.) (32F32) Geometric and analytic invariants on weakly pseudoconvex boundaries (32T27) Finite-type conditions for the boundary of a domain (32F18)

Related Items

Extension and restriction of holomorphic functions on convex finite type domains ⋮ Restriction of holomorphic functions on finite type domains in \({\mathbb{C}^{2}}\) ⋮ Extension from linear subvarieties for the Bergman scale of spaces on convex domains

Cites Work

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• On the extension of \(L^ 2\) holomorphic functions
• Extension and restriction of holomorphic functions on convex finite type domains
• Boundary invariants of pseudoconvex domains
• Convex hypersurfaces and Fourier transforms
• Zero varieties for the Nevanlinna class in convex domains of finite type in \(\mathbb{C}^n\)
• Henkin-Ramirez kernels with weight factors
• A formula for interpolation and division in \({\mathbb C}^n\).
• Support functions for convex domains of finite type
• Hölder estimates on convex domains of finite type
• Estimates on the Bergman kernels of convex domains
• Extension and restriction of holomorphic functions
• Hölder and \(L^p\) estimates for \(\overline {\partial}\) on convex domains of finite type depending on Catlin's multitype
• An alternative proof of an extension theorem of T. Ohsawa
• Extremal bases and Hölder estimates for \(\overline\partial\) on convex domains of finite type
• Convex domains of finite type
• Nonisotropic Hölder estimates on convex domains of finite type
• Extension problems in convex domains of finite type
• \(L^p\) estimates on convex domains of finite type
• Extension of bounded holomorphic functions in convex domains