Bulletin of the Belgian Mathematical Society - Simon Stevin

Radon inversion problem for holomorphic functions on strictly pseudoconvex domains

Piotr Kot

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Abstract

Let $p>0$ and let $\Omega\subset\Bbb C^{d}$ be a bounded, strictly pseudoconvex domain with boundary of class $C^{2}$. We consider a family of directions in the form of a continuous function $\gamma:\partial\Omega\times[0,1]\ni(z,t)\rightarrow\gamma(z,t)\in\overline{\Omega}$ satisfying some natural properties. Then for a given lower semicontinuous, strictly positive function $H$ on $\partial\Omega$ we construct a holomorphic function $f\in\Bbb O(\Omega)$ such that $H(z)=\int_{0}^{1}\left|f(\gamma(z,t))\right|^{p}dt$ for $\eta$-almost all $z\in\partial\Omega$ where $\eta$ is a given pro\-ba\-bility measure on $\partial\Omega$.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 17, Number 4 (2010), 623-640.

Dates
First available in Project Euclid: 24 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1290608191

Digital Object Identifier
doi:10.36045/bbms/1290608191

Mathematical Reviews number (MathSciNet)
MR2778441

Zentralblatt MATH identifier
1211.32003

Subjects
Primary: 32A05: Power series, series of functions 32A35: Hp-spaces, Nevanlinna spaces [See also 32M15, 42B30, 43A85, 46J15]

Keywords
Radon inversion problem Dirichlet problem exceptional sets

Citation

Kot, Piotr. Radon inversion problem for holomorphic functions on strictly pseudoconvex domains. Bull. Belg. Math. Soc. Simon Stevin 17 (2010), no. 4, 623--640. doi:10.36045/bbms/1290608191. https://projecteuclid.org/euclid.bbms/1290608191


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