Extensions of Hardy-Littlewood inequalities.
Finiteness problem for meromorphic mappings sharing n+3 hyperplanes of ℙⁿ(ℂ)
We prove some finiteness theorems for differential nondegenerate meromorphic mappings of into ℙⁿ(ℂ) which share n+3 hyperplanes.
Generalizations of inequalities of Littlewood and Paley.
Growth of functions in tubes.
Growth properties of entire functions depending on a parameter
We study the growth of parameter-dependent entire functions. We are mainly interested in the case where the functions depend holomorphically on the parameter.
Holomorphic Lipschitz functions and application to the -problem
Holomorphic Mappings in the Nevanlinna Class.
Interpolating sequences, Carleson measures and Wirtinger inequality
Let S be a sequence of points in the unit ball of ℂⁿ which is separated for the hyperbolic distance and contained in the zero set of a Nevanlinna function. We prove that the associated measure is bounded, by use of the Wirtinger inequality. Conversely, if X is an analytic subset of such that any δ -separated sequence S has its associated measure bounded by C/δⁿ, then X is the zero set of a function in the Nevanlinna class of . As an easy consequence, we prove that if S is a dual bounded sequence...
Interpolation on plane sets in C2
Invariant Meromorphic Functions on Complex Semisimple Lie Groups.
Le lemme fondamental de Nilsson dans le cas analytique local
On donne des évaluations précises de la croissance modérée des intégrales de fonctions de classe de Nilsson locale dans , exprimées par des caractéristiques topologiques des courbes de ramification des intégrands.
Lemme de Schwarz pour des produits cartésiens
Limit currents and value distribution of holomorphic maps
We construct -closed and -closed positive currents associated to a holomorphic map via cluster points of normalized weighted truncated image currents. They are constructed using analogues of the Ahlfors length-area inequality in higher dimensions. Such classes of currents are also referred to as Ahlfors currents. We give some applications to equidistribution problems in value distribution theory.
Lower bounds for norms of products of polynomials on spaces
For 1 < p < 2 we obtain sharp lower bounds for the uniform norm of products of homogeneous polynomials on , whenever the number of factors is no greater than the dimension of these Banach spaces (a condition readily satisfied in infinite-dimensional settings). The result also holds for the Schatten classes . For p > 2 we present some estimates on the constants involved.
Mean growth and Fourier coefficients of some classes of holomorphic functions on bounded symmetric domains
Meilleure approximation polynomiale et croissance des fonctions entières sur certaines variétés algébriques affines
Soit un compact polynomialement convexe de et son “potentiel logarithmique extrémal” dans . Supposons que est régulier (i.e. continue) et soit une fonction holomorphe sur un voisinage de . On construit alors une suite de polynôme de variables complexes avec deg pour , telle que l’erreur d’approximation soit contrôlée de façon assez précise en fonction du “pseudorayon de convergence” de par rapport à et du degré de convergence . Ce résultat est ensuite utilisé pour étendre...
Mesures de Monge-Ampère et caractérisation géométrique des variétés algébriques affines
Multiple values and uniqueness problem for meromorphic mappings sharing hyperplanes
The purpose of this article is to deal with multiple values and the uniqueness problem for meromorphic mappings from into the complex projective space ℙⁿ(ℂ) sharing hyperplanes. We obtain two uniqueness theorems which improve and extend some known results.
Nevanlinna-Cartan theory over function fields and a Diophantine equation.
Non-extendable holomorphic functions of bounded growth in Reinhardt domains