Zeros of bounded holomorphic functions in strictly pseudoconvex domains in ${ℂ}^2$

Arlebrink, Jim

Annales de l'Institut Fourier, Tome 43 (1993) no. 2, pp. 437-458.

Soit $D$ un domaine strictement pseudoconvexe borné dans ${ℂ}^2$, et soit $X$ un diviseur positif de $D$ d’aire finie. On montre l’existence d’une fonction bornée $f$ dont $X$ est l’ensemble des zéros de $f$. Ceci généralise un résultat de B. Berndtsson dans le cas où $D$ est la boule unité de ${ℂ}^2$.

Let $D$ be a bounded strictly pseudoconvex domain in ${ℂ}^2$ and let $X$ be a positive divisor of $D$ with finite area. We prove that there exists a bounded holomorphic function $f$ such that $X$ is the zero set of $f$. This result has previously been obtained by Berndtsson in the case where $D$ is the unit ball in ${ℂ}^2$.

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