Interpolation by holomorphic functions smooth to the boundary in the unit ball of \({\mathbb{C}}^ n\)

DOI10.1007/BF01458591zbMath0585.32018OpenAlexW1999930009MaRDI QIDQ1071138

Joaquim Bruna, Joaquin M. Ortega Aramburu

Publication date: 1986

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/164116

zbMATH Keywords

division propertyinterpolation setK-setalgebra of holomorphic functions in the unit ballnon-isotropic holomorphic jets

Mathematics Subject Classification ID

Continuation of analytic objects in several complex variables (32D15) Boundary behavior of holomorphic functions of several complex variables (32A40) Algebras of holomorphic functions of several complex variables (32A38)

Related Items

On holomorphic functions in the ball with absolutely continuous boundary values ⋮ Holomorphic approximation and estimates for the \({\bar \partial}\)-equation on strictly pseudoconvex nonsmooth domains ⋮ Unnamed Item ⋮ Interpolation along manifolds in Hardy-Sobolev spaces ⋮ Traces on curves of Sobolev spaces of holomorphic functions ⋮ On integral equations related to weighted Toeplitz operators ⋮ Maximum modulus sets and reflection sets ⋮ Unnamed Item ⋮ Peak sets and boundary interpolation sets for the unit disc: a survey ⋮ Traces of pluriharmonic functions on curves ⋮ Non-isotropic Gevrey classes in domains of finite type in \(\mathbb{C}^ 2\) ⋮ Gevrey interpolation in domains of finite type in \(\mathbb{C}^ 2\) ⋮ Extension of \(A^ t\)-jets from holomorphic submanifolds ⋮ Traces of pluriharmonic functions on the boundaries of analytic varieties

Cites Work

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• Cauchy transforms of measures, and a characterization of smooth peak interpolation sets for the ball algebra
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• Ensembles pics dans des domaines strictement pseudo-convexes
• Analyse harmonique non-commutative sur certains espaces homogènes. Etude de certaines intégrales singulières. (Non-commutative harmonic analysis on certain homogeneous spaces. Study of certain singular integrals.)
• The interpolating sets for \(A^ \infty\)
• Holomorphic approximation and hyperfunction theory on a C\(^1\) totally real submanifold of a complex manifold
• Boundary Interpolation Sets for Holomorphic Functions Smooth to the Boundary and BMO
• Singular integrals and estimates for the Cauchy-Riemann equations

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