On Gleason's Decomposition for A...(...).
On Hardy spaces in complex ellipsoids
This paper deals with atomic decomposition and factorization of functions in the holomorphic Hardy space . Such representation theorems have been proved for strictly pseudoconvex domains. The atomic decomposition has also been proved for convex domains of finite type. Here the Hardy space was defined with respect to the ordinary Euclidean surface measure on the boundary. But for domains of finite type, it is natural to define with respect to a certain measure that degenerates near Levi-flat points...
On Hardy spaces on worm domains
In this review article we present the problem of studying Hardy spaces and the related Szeg˝o projection on worm domains. We review the importance of the Diederich–Fornæss worm domain as a smooth bounded pseudoconvex domain whose Bergman projection does not preserve Sobolev spaces of sufficiently high order and we highlight which difficulties arise in studying the same problem for the Szeg˝o projection. Finally, we announce and discuss the results we have obtained so far in the setting of non-smooth...
On Hardy-Lipschitz spaces
On harmonic continuation of differentiable functions defined on a part of the boundary.
On -harmonic space .
On highly nonintegrable functions and homogeneous polynomials
We construct a sequence of homogeneous polynomials on the unit ball in which are big at each point of the unit sphere . As an application we construct a holomorphic function on which is not integrable with any power on the intersection of with any complex subspace.
On holomorphic isometries for the Kobayashi and Carathéodory distances on complex manifolds
It is shown that under certain conditions every holomorphic isometry for the Carathéodory or the Kobayashi distances is an isometry for the corrisponding metrics. These results are used to give a characterization of biholomorphic mappings between convex domains and complete circular domains.
On holomorphic maps between domains in
On hulls of meromorphy and a class of Stein manifolds
On ideals generated by bounded analytic functions in the bidisc
On Integral Representations and a priori Lipschitz Estimates for the Canonical Solution of the ...-Equation.
On -symmetrical functions
n the present paper the authors study some families of functions from a complex linear space into a complex linear space . They introduce the notion of -symmetrical function (; ) which is a generalization of the notions of even, odd and -symmetrical functions. They generalize the well know result that each function defined on a symmetrical subset of can be uniquely represented as the sum of an even function and an odd function.
On linear extension for interpolating sequences
Let A be a uniform algebra on X and σ a probability measure on X. We define the Hardy spaces and the interpolating sequences S in the p-spectrum of σ. We prove, under some structural hypotheses on A and σ, that if S is a “dual bounded” Carleson sequence, then S is -interpolating with a linear extension operator for s < p, provided that either p = ∞ or p ≤ 2. In the case of the unit ball of ℂⁿ we find, for instance, that if S is dual bounded in then S is -interpolating with a linear...
On locally convex extension of in the unit ball and continuity of the Bergman projection
We define locally convex spaces LW and HW consisting of measurable and holomorphic functions in the unit ball, respectively, with the topology given by a family of weighted-sup seminorms. We prove that the Bergman projection is a continuous map from LW onto HW. These are the smallest spaces having this property. We investigate the topological and algebraic properties of HW.
On -Bloch functions.
On matrix Reinhardt domains.
On M-Bloch Functions
On meromorphic functions with values in locally convex spaces
On M-harmonic space Bsp