Bounded holomorphic functions with given maximum modulus on all circles

DOI10.1090/S0002-9939-08-09468-9zbMath1157.32001WikidataQ118592655 ScholiaQ118592655MaRDI QIDQ3600597

Piotr Kot

Publication date: 5 February 2009

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

inner functionhomogeneous polynomialsmaximum modulus set

Mathematics Subject Classification ID

(H^p)-spaces, Nevanlinna spaces of functions in several complex variables (32A35) Power series, series of functions of several complex variables (32A05)

Related Items

About boundary values in $A(\Omega)$ ⋮ On analytic functions with divergent series of Taylor coefficients ⋮ Boundary functions on a bounded balanced domain ⋮ Radon inversion problem for holomorphic functions on circular, strictly convex domains ⋮ Unnamed Item ⋮ Approximation on slices in balanced strictly convex domains with \(C^2\) boundary

Cites Work

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• Inner functions and boundary values in \(H^\infty(\Omega)\) and \(A(\Omega)\) in smoothly bounded pseudoconvex domains
• Maximum modulus sets
• A peak set of Hausdorff dimension \(2n-1\) for the algebra \(A(D)\) in the boundary of a domain \(D\) with \(C^\infty\)-boundary in \(\mathbb C^n\).
• The Dimension of Peak-Interpolation Sets
• Homogeneous polynomials on strictly convex domains

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