Radon inversion problem for holomorphic functions on strictly pseudoconvex domains
Kot, Piotr
Bull. Belg. Math. Soc. Simon Stevin, Tome 17 (2010) no. 1, p. 623-640 / Harvested from Project Euclid
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 $\partial\Omega$.
Publié le : 2010-08-15
Classification:  Radon inversion problem,  Dirichlet problem,  exceptional sets,  32A05,  32A35
@article{1290608191,
     author = {Kot, Piotr},
     title = {Radon inversion problem for holomorphic functions on strictly pseudoconvex
domains},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {17},
     number = {1},
     year = {2010},
     pages = { 623-640},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1290608191}
}
Kot, Piotr. Radon inversion problem for holomorphic functions on strictly pseudoconvex
domains. Bull. Belg. Math. Soc. Simon Stevin, Tome 17 (2010) no. 1, pp.  623-640. http://gdmltest.u-ga.fr/item/1290608191/