Dans cet article, nous étudions les zéros des fonctions holomorphes dans le bidisque dont le logarithme du module vérifie une condition de croissance : nous caractérisons par une condition de type Blaschke les zéros des fonctions vérifiant$${\int }_{D^2}{\delta }_{\partial D^2}(z{)}^{\alpha }{log}^{+}\left|f\left(z\right)\right|d\lambda \left(z\right)\<\infty ,$$pour $\alpha \>-1$, et nous donnons les conditions suffisantes pour des classes plus petites, en particulier pour la classe de Nevanlinna du bidisque.

We obtain an extension of Jack-Miller-Mocanu’s Lemma for holomorphic mappings defined in some Reinhardt domains in ${ℂ}^n$. Using this result we consider first and second order partial differential subordinations for holomorphic mappings defined on the Reinhardt domain $B_{2p}$ with p ≥ 1.

Let Ω be a C∞-domain in Cn. It is well known that a holomorphic function on Ω behaves twice as well in complex tangential directions (see [GS] and [Kr] for instance). It follows from well known results (see [H], [RS]) that some converse is true for any kind of regular functions when Ω satisfies(P)    The real tangent space is generated by the Lie brackets of real and imaginary parts of complex tangent vectorsIn this paper we are interested in the behavior of holomorphic Hardy-Sobolev functions in...