-regularity for the -equation on a piecewise smooth union of strictly pseudoconvex domains in
Joachim Michel, Alessandro Perotti (1994)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Joachim Michel, Alessandro Perotti (1994)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Chin-Huei Chang, Hsuan-Pei Lee (2006)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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The Hartogs Theorem for holomorphic functions is generalized in two settings: a CR version (Theorem 1.2) and a corresponding theorem based on it for -closed forms at the critical degree, (Theorem 1.1). Part of Frenkel’s lemma in category is also proved.
Alberto Scalari (1997)
Rendiconti del Seminario Matematico della Università di Padova
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Vincent Thilliez (1998)
Publicacions Matemàtiques
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We introduce an alternative proof of the existence of certain C barrier maps, with polynomial explosion of the derivatives, on weakly pseudoconvex domains in C. Barriers of this sort have been constructed very recently by J. Michel and M.-C. Shaw, and have various applications. In our paper, the adaptation of Hörmander's L techniques to suitable vector-valued functions allows us to give a very simple approach of the problem and to improve some aspects of the result of Michel and Shaw,...
Telemachos Hatziafratis (1990)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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C. H. Chang, H. P. Lee (1999)
Publicacions Matemàtiques
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Let M be an open subset of a compact strongly pseudoconvex hypersurface {ρ = 0} defined by M = D × C ∩ {ρ = 0}, where 1 ≤ m ≤ n-2, D = {σ(z, ..., z) < 0} ⊂ C is strongly pseudoconvex in C. For ∂ closed (0, q) forms f on M, we prove the semi-global existence theorem for ∂ if 1 ≤ q ≤ n-m-2, or if q = n - m - 1 and f satisfies an additional “moment condition”. Most importantly, the solution operator satisfies L estimates for 1 ≤ p ≤ ∞ with p = 1 and ∞ included.
Klas Diederich, Emmanuel Mazzilli (1997)
Annales de l'institut Fourier
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Strong pathologies with respect to growth properties can occur for the extension of holomorphic functions from submanifolds of pseudoconvex domains to all of even in quite simple situations; The spaces are, in general, not at all preserved. Also the image of the Hilbert space under the restriction to can have a very strange structure.