The -Neumann operator on strongly pseudoconvex domain with piecewise smooth boundary
Osama Abdelkader, Sayed Saber (2005)
Mathematica Slovaca
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Osama Abdelkader, Sayed Saber (2005)
Mathematica Slovaca
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Kolář, Martin
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Let be a domain with smooth boundary and . A holomorphic function on is called a () peak function at if , , and for all . If is strongly pseudoconvex, then peak functions exist. On the other hand, J. E. Fornaess constructed an example in to show that this result fails, even for functions, on a weakly pseudoconvex domain [Math. Ann. 227, 173-175 (1977; Zbl 0346.32026)]. Subsequently, E. Bedford and J. E. Fornaess showed that there is always a continuous peak function...
Gregor Herbort (2014)
Annales Polonici Mathematici
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Let D be a smooth bounded pseudoconvex domain in ℂⁿ of finite type. We prove an estimate on the pluricomplex Green function of D that gives quantitative information on how fast the Green function vanishes if the pole w approaches the boundary. Also the Hölder continuity of the Green function is discussed.
Romi F. Shamoyan, Olivera R. Mihić (2016)
Czechoslovak Mathematical Journal
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We present new sharp embedding theorems for mixed-norm analytic spaces in pseudoconvex domains with smooth boundary. New related sharp results in minimal bounded homogeneous domains in higher dimension are also provided. Last domains we consider are domains which are direct generalizations of the well-studied so-called bounded symmetric domains in Our results were known before only in the very particular case of domains of such type in the unit ball. As in the unit ball case, all our...
Joachim Michel, Alessandro Perotti (1994)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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R. Range (1995)
Banach Center Publications
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In this survey we shall tour the area of multidimensional complex analysis which centers around ∂̅-problems (i.e., the Cauchy-Riemann equations) on pseudoconvex domains. Along the way we shall highlight some of the classical milestones as well as more recent landmarks, and we shall discuss some of the major open problems and conjectures. For the sake of simplicity we will only consider domains in ; intriguing phenomena occur already in the simple setting of (Euclidean) convex domains....
Linus Carlsson (2008)
Mathematica Bohemica
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Pseudoconvex domains are exhausted in such a way that we keep a part of the boundary fixed in all the domains of the exhaustion. This is used to solve a problem concerning whether the generators for the ideal of either the holomorphic functions continuous up to the boundary or the bounded holomorphic functions, vanishing at a point in where the fibre is nontrivial, has to exceed . This is shown not to be the case.