Note on integral representation of holomorphic functions in several complex variables
Chen Shu-Jin (1989)
Rendiconti del Seminario Matematico della Università di Padova
Similarity:
Chen Shu-Jin (1989)
Rendiconti del Seminario Matematico della Università di Padova
Similarity:
Joaquín M. Ortega, Joan Fàbrega (1992)
Publicacions Matemàtiques
Similarity:
Let D be a bounded strictly pseudoconvex domain of Cn with C ∞ boundary and Y = {z; u1(z) = ... = ul(z) = 0} a holomorphic submanifold in the neighbourhood of D', of codimension l and transversal to the boundary of D. In this work we give a decomposition formula f = u1f1 + ... + ulfl for functions f of the Bergman-Sobolev...
Jakóbczak, Piotr (1993)
Portugaliae mathematica
Similarity:
Wilhelm Klingenberg (1990)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Similarity:
Jaroslav Fuka (1983)
Banach Center Publications
Similarity:
E. L. Stout (1973)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Similarity:
Sandrine Grellier (1993)
Revista Matemática Iberoamericana
Similarity:
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 vectors ...
Patrick Ahern, Joaquim Bruna (1988)
Revista Matemática Iberoamericana
Similarity:
In this paper we deal with several characterizations of the Hardy-Sobolev spaces in the unit ball of C, that is, spaces of holomorphic functions in the ball whose derivatives up to a certain order belong to the classical Hardy spaces. Some of our characterizations are in terms of maximal functions, area functions or Littlewood-Paley functions involving only complex-tangential derivatives. A special case of our results is a characterization of H itself involving only complex-tangential...
Laurent Stolovitch (2005)
Publications Mathématiques de l'IHÉS
Similarity:
Let X be a germ of holomorphic vector field at the origin of and vanishing there. We assume that X is a good perturbation of a “nondegenerate” singular completely integrable system. The latter is associated to a family of linear diagonal vector fields which is assumed to have nontrivial polynomial first integrals (they are generated by the so called “resonant monomials”). We show that X admits many invariant analytic subsets in a neighborhood of the origin. These are...