Intégrales singulières holomorphes
Let be a compact subset of an hyperconvex open set , forming with D a Runge pair and such that the extremal p.s.h. function ω(·,K,D) is continuous. Let H(D) and H(K) be the spaces of holomorphic functions respectively on D and K equipped with their usual topologies. The main result of this paper contains as a particular case the following statement: if T is a continuous linear map of H(K) into H(K) whose restriction to H(D) is continuous into H(D), then the restriction of T to is a continuous...
We prove, among other results, that is plurisubharmonic (psh) when belong to a family of functions in where is the -Lipchitz functional space with Then we establish a new characterization of holomorphic functions defined on open sets of
In 1984 L. Lempert showed that the Lempert function and the Carathéodory distance coincide on non-planar bounded strongly linearly convex domains with real-analytic boundaries. Following his paper, we present a slightly modified and more detailed version of the proof. Moreover, the Lempert Theorem is proved for non-planar bounded strongly linearly convex domains.
In this paper we extend the definition of the linearly invariant family and the definition of the universal linearly invariant family to higher dimensional case. We characterize these classes and give some of their properties. We also give a relationship of these families with the Bloch space.
We generalize some criteria of boundedness of -index in joint variables for in a bidisc analytic functions. Our propositions give an estimate the maximum modulus on a skeleton in a bidisc and an estimate of th partial derivative by lower order partial derivatives (analogue of Hayman’s theorem).