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Complex tangential characterizations of Hardy-Sobolev spaces of holomorphic functions.

Sandrine Grellier (1993)

Revista Matemática Iberoamericana

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...

Complexité et géométrie réelle

Jean-Jacques Risler (1984/1985)

Séminaire Bourbaki

Complex-Tangential Sets and Boundary Values in Submanifolds of the Boundary.

A. Noell, W.C. Ramey, D.C. Ullrich (1987)

Mathematische Zeitschrift

Composition of Potentials with Inner Functions.

Manfred Stoll (1992)

Mathematica Scandinavica

Composition operators from the weighted Bergman space to the $n$ th weighted spaces on the unit disc.

Stević, Stevo (2009)

Discrete Dynamics in Nature and Society

Condition polynomiale de Leja et L-régularité dans $C^{n}$

Nguyen Thanh Van (1985)

Annales Polonici Mathematici

Conditions for the $\bar{\partial}$ -closedness of differential forms.

Kytmanov, A.M., Myslivets, S.G. (2009)

Sibirskij Matematicheskij Zhurnal

Conical Fourier-Borel transformations for harmonic functionals on the Lie ball

Mitsuo Morimoto, Keiko Fujita (1996)

Banach Center Publications

Let L(z) be the Lie norm on $\tilde{} = ℂ^{n + 1}$ and L*(z) the dual Lie norm. We denote by $_{Δ} (\tilde{B} (R))$ the space of complex harmonic functions on the open Lie ball $\tilde{B} (R)$ and by $E x p_{Δ} (\tilde{}; (A, L *))$ the space of entire harmonic functions of exponential type (A,L*). A continuous linear functional on these spaces will be called a harmonic functional or an entire harmonic functional. We shall study the conical Fourier-Borel transformations on the spaces of harmonic functionals or entire harmonic functionals.

Constructibilité des solutions des systèmes microdifférentiels

Teresa Monteiro-Fernandes (1982)

Journées équations aux dérivées partielles

Construction d’hypersurfaces irréductibles avec lieu singulier donné dans $ℂ^{n}$

Jean-Pierre Demailly (1980)

Annales de l'institut Fourier

Étant donné un ensemble analytique $S$ de codimension $\geq 2$ dans $C^{n}$ , nous construisons des hypersurfaces irréductibles de lieu singulier $S$ , avec contrôle de la croissance. À partir d’un contre-exemple au problème de Bezout transcendant, dû à M. Cornalba et B. Shiffman, nous montrons l’existence d’une courbe irréductible d’ordre 0 dans $C^{2}$ , dont le lieu singulier est d’ordre infini. Nous étudions également en application certaines propriétés arithmétiques de l’anneau de convolution $ℰ^{'} (R^{n}) .$

Construction of boundary invariants and the logarithmic singularity of the Bergman kernel.

Hirachi, Kengo (2000)

Annals of Mathematics. Second Series

Constructions de fonctions holomorphes bornées

N. Sibony (1982/1983)

Séminaire Équations aux dérivées partielles (Polytechnique)

Continuation of holomorphic functions with growth conditions and some of its applications

Alexander V. Abanin, Pham Trong Tien (2010)

Studia Mathematica

We prove a generalization of the well-known Hörmander theorem on continuation of holomorphic functions with growth conditions from complex planes in $ℂ^{p}$ into the whole $ℂ^{p}$ . We apply this result to construct special families of entire functions playing an important role in convolution equations, interpolation and extension of infinitely differentiable functions from closed sets. These families, in their turn, are used to study optimal or canonical, in a certain sense, weight sequences defining inductive...

Continuity of intersection of analytic sets

P. Tworzewski, T. Winiarski (1983)

Annales Polonici Mathematici

Contribution effective dans le réel

D. Barlet (1985)

Compositio Mathematica

Convergence in nonisotropic regions of harmonic functions in $^{n}$

Carme Cascante, Joaquin Ortega (1999)