Displaying similar documents to “On the Djrbashian kernel of a Siegel domain”

Bergman function, Genchev transform and L²-angles, for multidimensional tubes

Hyb Wojciech

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CONTENTS1. Introduction.......................................................................................................52. Basic definitions, notations and facts................................................................63. Definitions of the Genchev transform................................................................84. Basic properties of the Genchev transform......................................................115. Some properties of the weight w B ..............................................................166....

Proper holomorphic liftings and new formulas for the Bergman and Szegő kernels

E. H. Youssfi (2002)

Studia Mathematica

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We consider a large class of convex circular domains in M m , n ( ) × . . . × M m d , n d ( ) which contains the oval domains and minimal balls. We compute their Bergman and Szegő kernels. Our approach relies on the analysis of some proper holomorphic liftings of our domains to some suitable manifolds.

An example of a pseudoconvex domain whose holomorphic sectional curvature of the Bergman metric is unbounded

Gregor Herbort (2007)

Annales Polonici Mathematici

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Let a and m be positive integers such that 2a < m. We show that in the domain D : = z ³ | r ( z ) : = z + | z | ² + | z | 2 m + | z z | 2 a + | z | 2 m < 0 the holomorphic sectional curvature R D ( z ; X ) of the Bergman metric at z in direction X tends to -∞ when z tends to 0 non-tangentially, and the direction X is suitably chosen. It seems that an example with this feature has not been known so far.

Weighted Bergman projections and tangential area integrals

William Cohn (1993)

Studia Mathematica

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Let Ω be a bounded strictly pseudoconvex domain in n . In this paper we find sufficient conditions on a function f defined on Ω in order that the weighted Bergman projection P s f belong to the Hardy-Sobolev space H k p ( Ω ) . The conditions on f we consider are formulated in terms of tent spaces and complex tangential vector fields. If f is holomorphic then these conditions are necessary and sufficient in order that f belong to the Hardy-Sobolev space H k p ( Ω ) .

Zeros of bounded holomorphic functions in strictly pseudoconvex domains in 2

Jim Arlebrink (1993)

Annales de l'institut Fourier

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Let D be a bounded strictly pseudoconvex domain in 2 and let X be a positive divisor of D with finite area. We prove that there exists a bounded holomorphic function f such that X is the zero set of f . This result has previously been obtained by Berndtsson in the case where D is the unit ball in 2 .

Hilbert-Schmidt Hankel operators with anti-holomorphic symbols on complete pseudoconvex Reinhardt domains

Mehmet Çelik, Yunus E. Zeytuncu (2017)

Czechoslovak Mathematical Journal

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On complete pseudoconvex Reinhardt domains in 2 , we show that there is no nonzero Hankel operator with anti-holomorphic symbol that is Hilbert-Schmidt. In the proof, we explicitly use the pseudoconvexity property of the domain. We also present two examples of unbounded non-pseudoconvex domains in 2 that admit nonzero Hilbert-Schmidt Hankel operators with anti-holomorphic symbols. In the first example the Bergman space is finite dimensional. However, in the second example the Bergman...

Weighted L -estimates for Bergman projections

José Bonet, Miroslav Engliš, Jari Taskinen (2005)

Studia Mathematica

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We consider Bergman projections and some new generalizations of them on weighted L ( ) -spaces. A new reproducing formula is obtained. We show the boundedness of these projections for a large family of weights v which tend to 0 at the boundary with a polynomial speed. These weights may even be nonradial. For logarithmically decreasing weights bounded projections do not exist. In this case we instead consider the projective description problem for holomorphic inductive limits.

Pointwise estimates for the weighted Bergman projection kernel in n , using a weighted L 2 estimate for the ¯ equation

Henrik Delin (1998)

Annales de l'institut Fourier

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Weighted L 2  estimates are obtained for the canonical solution to the equation in L 2 ( n , e - φ d λ ) , where Ω is a pseudoconvex domain, and φ is a strictly plurisubharmonic function. These estimates are then used to prove pointwise estimates for the Bergman projection kernel in L 2 ( n , e - φ d λ ) . The weight is used to obtain a factor e - ϵ ρ ( z , ζ ) in the estimate of the kernel, where ρ is the distance function in the Kähler metric given by the metric form i φ .

Henkin-Ramirez formulas with weight factors

B. Berndtsson, Mats Andersson (1982)

Annales de l'institut Fourier

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We construct a generalization of the Henkin-Ramírez (or Cauchy-Leray) kernels for the -equation. The generalization consists in multiplication by a weight factor and addition of suitable lower order terms, and is found via a representation as an “oscillating integral”. As special cases we consider weights which behave like a power of the distance to the boundary, like exp- ϕ with ϕ convex, and weights of polynomial decrease in C n . We also briefly consider kernels with singularities on...

Iterates and the boundary behavior of the Berezin transform

Jonathan Arazy, Miroslav Engliš (2001)

Annales de l’institut Fourier

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Let μ be a measure on a domain Ω in n such that the Bergman space of holomorphic functions in L 2 ( Ω , μ ) possesses a reproducing kernel K ( x , y ) and K ( x , x ) &gt; 0 x Ω . The Berezin transform associated to μ is the integral operator B f ( y ) = K ( y , y ) - 1 Ω f ( x ) | K ( x , y ) | 2 d μ ( x ) . The number B f ( y ) can be interpreted as a certain mean value of f around y , and functions satisfying B f = f as functions having a certain mean-value property. In this paper we investigate the boundary behavior of B f , the existence of functions f satisfying...

Subharmonicity properties of the Bergman kernel and some other functions associated to pseudoconvex domains

Bo Berndtsson (2006)

Annales de l’institut Fourier

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Let D be a pseudoconvex domain in t k × z n and let φ be a plurisubharmonic function in D . For each t we consider the n -dimensional slice of D , D t = { z ; ( t , z ) D } , let φ t be the restriction of φ to D t and denote by K t ( z , ζ ) the Bergman kernel of D t with the weight function φ t . Generalizing a recent result of Maitani and Yamaguchi (corresponding to n = 1 and φ = 0 ) we prove that log K t ( z , z ) is a plurisubharmonic function in D . We also generalize an earlier results of Yamaguchi concerning the Robin function and discuss similar results in...