Bulletin of the Belgian Mathematical Society - Simon Stevin

Radon inversion problem for holomorphic functions on strictly pseudoconvex domains

Piotr Kot

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

https://projecteuclid.org/euclid.bbms/1290608191

Digital Object Identifier
doi:10.36045/bbms/1290608191

Mathematical Reviews number (MathSciNet)
MR2778441

Zentralblatt MATH identifier
1211.32003

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