spaces on bounded symmetric domains
Kyong T. Hahn, Josephine Mitchell (1973)
Annales Polonici Mathematici
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Kyong T. Hahn, Josephine Mitchell (1973)
Annales Polonici Mathematici
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Gabriela Kohr, Mirela Kohr (1997)
Annales Polonici Mathematici
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We obtain an extension of Jack-Miller-Mocanu’s Lemma for holomorphic mappings defined in some Reinhardt domains in . Using this result we consider first and second order partial differential subordinations for holomorphic mappings defined on the Reinhardt domain with p ≥ 1.
Le Mau Hai, Tang Van Long (2002)
Studia Mathematica
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The aim of this paper is to establish the equivalence between the non-pluripolarity of a compact set in a complex space and the property for the dual space of the space of germs of holomorphic functions on that compact set.
Diana D. Jiménez S., Lino F. Reséndis O., Luis M. Tovar S. (2014)
Banach Center Publications
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Following the line of Ouyang et al. (1998) to study the spaces of holomorphic functions in the unit ball of ℂⁿ, we present in this paper several results and relations among , the α-Bloch, the Dirichlet and the little spaces.
B. Platynowicz (1980)
Matematički Vesnik
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Marek Jarnicki, Peter Pflug (2003)
Annales Polonici Mathematici
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Let be a pseudoconvex domain and let be a locally pluriregular set, j = 1,...,N. Put . Let U be an open connected neighborhood of X and let M ⊊ U be an analytic subset. Then there exists an analytic subset M̂ of the “envelope of holomorphy” X̂ of X with M̂ ∩ X ⊂ M such that for every function f separately holomorphic on X∖M there exists an f̂ holomorphic on X̂∖M̂ with . The result generalizes special cases which were studied in [Ökt 1998], [Ökt 1999], [Sic 2001], and [Jar-Pfl 2001]. ...
Marek Jarnicki, Peter Pflug (1997)
Annales Polonici Mathematici
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We present various characterizations of n-circled domains of holomorphy with respect to some subspaces of .
Edgar Lee Stout (2006)
Annales Polonici Mathematici
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We construct a domain of holomorphy in , N≥ 2, whose envelope of holomorphy is not diffeomorphic to a domain in .
Е.М. Кузнецова (1986)
Trudy Geometriceskogo Seminara
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Ngaiming Mok (2012)
Journal of the European Mathematical Society
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We study the extension problem for germs of holomorphic isometries up to normalizing constants between bounded domains in Euclidean spaces equipped with Bergman metrics on and on . Our main focus is on boundary extension for pairs of bounded domains such that the Bergman kernel extends meromorphically in to a neighborhood of , and such that the analogous statement holds true for the Bergman kernel on . Assuming that and are complete Kähler manifolds, we prove that...
Anahit Harutyunyan, Wolfgang Lusky (2010)
Studia Mathematica
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We study the spaces where Ω is a disc with radius R and μ is a given probability measure on [0,R[. We show that, depending on μ, is either isomorphic to l₁ or to . Here Aₙ is the space of all polynomials of degree ≤ n endowed with the L₁-norm on the unit sphere.
Nabil Ourimi (2002)
Annales Polonici Mathematici
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The purpose of this paper is to prove that proper holomorphic self-mappings of the minimal ball are biholomorphic. The proof uses the scaling technique applied at a singular point and relies on the fact that a proper holomorphic mapping f: D → Ω with branch locus is factored by automorphisms if and only if is a normal subgroup of for some and .
A. Zięba (1972)
Colloquium Mathematicae
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Rafał Czyż (2009)
Annales Polonici Mathematici
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Let be a bounded hyperconvex domain in and set , j=1,...,s, s ≥ 3. Also let be the image of D under the proper holomorphic map π. We characterize those continuous functions that can be extended to a real-valued pluriharmonic function in .
M. Jevtić (1985)
Matematički Vesnik
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J. Siciak (1985)
Matematički Vesnik
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Marcin Bilski (2012)
Annales Polonici Mathematici
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Let X be an analytic set defined by polynomials whose coefficients are holomorphic functions. We formulate conditions on sequences of holomorphic functions converging locally uniformly to , respectively, such that the sequence of sets obtained by replacing ’s by ’s in the polynomials converges to X.
Makhlouf Derridj, John Erik Fornaess (1983)
Annales de l'institut Fourier
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Let an open set in near , a suitable holomorphic function near . If we know that we can solve the following problem (see [M. Derridj, Annali. Sci. Norm. Pisa, Série IV, vol. IX (1981)]) : , ( is a form, closed in in with supp, then we deduce an extension result for functions on , as holomorphic fonctions in .
Nguyen Quang Dieu, Phung Van Manh (2014)
Annales Polonici Mathematici
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Let F be the Cartesian product of N closed sets in ℂ. We prove that there exists a function g which is continuous on F and holomorphic on the interior of F such that is complete pluripolar in . Using this result, we show that if D is an analytic polyhedron then there exists a bounded holomorphic function g such that is complete pluripolar in . These results are high-dimensional analogs of the previous ones due to Edlund [Complete pluripolar curves and graphs, Ann. Polon. Math....
Viorel Vâjâitu (2016)
Czechoslovak Mathematical Journal
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We consider a convexity notion for complex spaces with respect to a holomorphic line bundle over . This definition has been introduced by Grauert and, when is analytically trivial, we recover the standard holomorphic convexity. In this circle of ideas, we prove the counterpart of the classical Remmert’s reduction result for holomorphically convex spaces. In the same vein, we show that if separates each point of , then can be realized as a Riemann domain over the complex projective...
María D. Acosta, Mary Lilian Lourenço (2007)
Studia Mathematica
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Let be the Banach space of all bounded and continuous functions on the closed unit ball of a complex Banach space X and holomorphic on the open unit ball, with sup norm, and let be the subspace of of those functions which are uniformly continuous on . A subset is a boundary for if for every . We prove that for X = d(w,1) (the Lorentz sequence space) and X = C₁(H), the trace class operators, there is a minimal closed boundary for . On the other hand, for X = , the Schreier...
William Alexandre, Emmanuel Mazzilli (2014)
Annales de l’institut Fourier
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We give in a real analytic almost complex structure , a real analytic hypersurface and a vector in the Levi null set at of , such that there is no germ of -holomorphic disc included in with and , although the Levi form of has constant rank. Then for any hypersurface and any complex structure , we give sufficient conditions under which there exists such a germ of disc.
Jürgen Leiterer (2007)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Let be a holomorphic Banach bundle over a compact complex manifold, which can be defined by a cocycle of holomorphic transition functions with values of the form where is compact. Assume that the characteristic fiber of has the compact approximation property. Let be the complex dimension of and . Then: If is a holomorphic vector bundle (of finite rank) with , then . In particular, if , then .