On n-circled -domains of holomorphy
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 .
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 .
Marek Jarnicki, Peter Pflug (2006)
Studia Mathematica
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Let X be a Riemann domain over . If X is a domain of holomorphy with respect to a family ℱ ⊂(X), then there exists a pluripolar set such that every slice of X with a∉ P is a region of holomorphy with respect to the family .
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 .
A. Zięba (1972)
Colloquium Mathematicae
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William Fleissner, Lynne Yengulalp (2013)
Fundamenta Mathematicae
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Let M be a metrizable group. Let G be a dense subgroup of . We prove that if G is domain representable, then . The following corollaries answer open questions. If X is completely regular and is domain representable, then X is discrete. If X is zero-dimensional, T₂, and is subcompact, then X is discrete.
Sayed Saber (2015)
Czechoslovak Mathematical Journal
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Let be a Stein manifold of complex dimension and be a relatively compact domain with smooth boundary in . Assume that is a weakly -pseudoconvex domain in . The purpose of this paper is to establish sufficient conditions for the closed range of on . Moreover, we study the -problem on . Specifically, we use the modified weight function method to study the weighted -problem with exact support in . Our method relies on the -estimates by Hörmander (1965) and by Kohn (1973). ...
M. Prizzi, M. Rinaldi, K. P. Rybakowski (2002)
Studia Mathematica
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Consider the family uₜ = Δu + G(u), t > 0, , , t > 0, , of semilinear Neumann boundary value problems, where, for ε > 0 small, the set is a thin domain in , possibly with holes, which collapses, as ε → 0⁺, onto a (curved) k-dimensional submanifold of . If G is dissipative, then equation has a global attractor . We identify a “limit” equation for the family , prove convergence of trajectories and establish an upper semicontinuity result for the family as ε → 0⁺. ...
Gregor Fels, Alan Huckleberry (2005)
Bulletin de la Société Mathématique de France
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A real form of a complex semi-simple Lie group has only finitely many orbits in any given -flag manifold . The complex geometry of these orbits is of interest, e.g., for the associated representation theory. The open orbits generally possess only the constant holomorphic functions, and the relevant associated geometric objects are certain positive-dimensional compact complex submanifolds of which, with very few well-understood exceptions, are parameterized by the Wolf cycle...
Karl Oeljeklaus, Dan Zaffran (2006)
Bulletin de la Société Mathématique de France
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Let denote a holomorphic bundle with fiber and with basis . Both and are assumed to be Stein. For a Reinhardt bounded domain of dimension or , we give a necessary and sufficient condition on for the existence of a non-Stein such (Theorem ); for , we give necessary and sufficient criteria for to be Stein (Theorem ). For a Reinhardt bounded domain of any dimension not intersecting any coordinate hyperplane, we give a sufficient criterion for to be Stein (Theorem...
Alessandro Perotti (1986)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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Viene studiata l'equazione per le forme regolari sulla chiusura dell'intersezione di domini pseudoconvessi. Si costruisce un operatore soluzione in forma integrale e sotto ipotesi opportune si ottengono stime della soluzione nelle norme .
J. Siciak (1985)
Matematički Vesnik
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Dorothee D. Haroske, Leszek Skrzypczak (2013)
Studia Mathematica
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We study embeddings of spaces of Besov-Morrey type, , where is a bounded domain, and obtain necessary and sufficient conditions for the continuity and compactness of . This continues our earlier studies relating to the case of . Moreover, we also characterise embeddings into the scale of spaces or into the space of bounded continuous functions.
Jiecheng Chen, Dashan Fan, Yiming Ying (2002)
Studia Mathematica
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We give some rather weak sufficient condition for boundedness of the Marcinkiewicz integral operator on the product spaces (1 < p < ∞), which improves and extends some known results.
Christian Samuel (2010)
Colloquium Mathematicae
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We show that every operator from to is compact when 1 ≤ p,q < s and that every operator from to is compact when 1/p + 1/q > 1 + 1/s.
Jiří Souček (1972)
Časopis pro pěstování matematiky
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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...
Shaban Khidr, Osama Abdelkader (2017)
Czechoslovak Mathematical Journal
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Let be a -convex intersection, , , in a complex manifold of complex dimension , , and let be a holomorphic vector bundle of rank over . In this paper, -estimates, , for solutions to the -equation with small loss of smoothness are obtained for -valued -forms on when . In addition, we solve the -equation with a support condition in -spaces. More precisely, we prove that for a -closed form in , , , with compact support and for with there...
Abtin Daghighi, Frank Wikström (2016)
Czechoslovak Mathematical Journal
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Let be a bounded, simply connected -convex domain. Let and let be a function on which is separately -smooth with respect to (by which we mean jointly -smooth with respect to , ). If is -analytic on , then is -analytic on . The result is well-known for the case , , even when a priori is only known to be continuous.
Yoel Feler (2008)
Journal of the European Mathematical Society
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Let denote either or . We study certain analytic properties of the space of ordered geometrically generic -point configurations in . This space consists of all such that no of the points belong to a hyperplane in . In particular, we show that for a big enough any holomorphic map commuting with the natural action of the symmetric group in is of the form , , where is an -invariant holomorphic map. A similar result holds true for mappings of the configuration...
Tamás Erdélyi (2003)
Studia Mathematica
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Denote by spanf₁,f₂,... the collection of all finite linear combinations of the functions f₁,f₂,... over ℝ. The principal result of the paper is the following. Theorem (Full Clarkson-Erdős-Schwartz Theorem). Suppose is a sequence of distinct positive numbers. Then is dense in C[0,1] if and only if . Moreover, if , then every function from the C[0,1] closure of can be represented as an analytic function on z ∈ ℂ ∖ (-∞, 0]: |z| < 1 restricted to (0,1). This result improves an...
Hans Triebel (1994)
Studia Mathematica
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Let , where the sum is taken over the lattice of all points k in having integer-valued components, j∈ℕ and . Let be either or (s ∈ ℝ, 0 < p < ∞, 0 < q ≤ ∞) on The aim of the paper is to clarify under what conditions is equivalent to .