scholarly journals L∞-Estimates of the Bergman projection in the Lie ball ofℂn

2011 ◽  
Vol 9 (2) ◽  
pp. 109-128 ◽  
Author(s):  
Cyrille Nana
Keyword(s):  
Bergman Projection ◽  
The Other ◽  
Bounded Domains ◽  
Cayley Transform ◽  
Bounded Symmetric Domains ◽  
Bergman Projections

In this paper, we consider estimates with loss for the Bergman projections of bounded symmetric domains ofℂnin their Harish-Chandra realizations. This paper is twofold: on one side we develop transfer methods between these bounded domains and their Cayley transform; on the other side we give a new range ofqsuch that the Bergman projection is bounded fromL∞(ℬn)toLq(ℬn)whereℬnis the Lie ball ofℂn.

scholarly journals On Extremal Problems in Certain New Bergman Type Spaces in Some Bounded Domains inCn

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Romi F. Shamoyan ◽  
Olivera Mihić
Keyword(s):  
Unit Disk ◽  
Bergman Kernel ◽  
Extremal Problems ◽  
Bergman Projection ◽  
Bounded Domains ◽  
Bounded Symmetric Domains ◽  
Siegel Domains ◽  
Type Spaces ◽  
Tube Type ◽  
Homogeneous Domains

Based on recent results on boundedness of Bergman projection with positive Bergman kernel in analytic spaces in various types of domains inCn, we extend our previous sharp results on distances obtained for analytic Bergman type spaces in unit disk to some new Bergman type spaces in Lie ball, bounded symmetric domains of tube type, Siegel domains, and minimal bounded homogeneous domains.

Mapping properties of the Bergman projections on elementary Reinhardt domains

2021 ◽  
Vol 71 (4) ◽  
pp. 831-844
Author(s):  
Shuo Zhang
Keyword(s):  
Sobolev Spaces ◽  
Bergman Projection ◽  
Reinhardt Domain ◽  
Reinhardt Domains ◽  
Multi Index ◽  
Bergman Projections

Abstract The elementary Reinhardt domain associated to multi-index k = (k 1, …, k n ) ∈ ℤ n is defined by ℋ ( k ) : = { z ∈ D n : z k   is defined and   | z k | < 1 } . $$\mathcal{H}(\mathbf{k}):=\{z\in\mathbb{D}^n: z^{\mathbf{k}}\ \text{is defined and}\ |z^{\mathbf{k}}|<1\}.$$ In this paper, we study the mapping properties of the associated Bergman projection on L p spaces and L p Sobolev spaces of order ≥ 1.

ELLIPTIC EQUATIONS IN ℝ2 WITH ONE-SIDED EXPONENTIAL GROWTH

2004 ◽  
Vol 06 (06) ◽  
pp. 947-971 ◽  
Author(s):  
ZHITAO ZHANG ◽  
MARTA CALANCHI ◽  
BERNHARD RUF
Keyword(s):  
Exponential Growth ◽  
Elliptic Equations ◽  
Morse Index ◽  
Linear Growth ◽  
Critical Growth ◽  
The Other ◽  
Critical Groups ◽  
Bounded Domains ◽  
Eigen Value

We consider elliptic equations in bounded domains Ω⊂ℝ2 with nonlinearities which have exponential growth at +∞ (subcritical and critical growth, respectively) and linear growth λ at -∞, with λ>λ1, the first eigen value of the Laplacian. We prove that such equations have at least two solutions for certain forcing terms; one solution is negative, the other one is sign-changing. Some critical groups and Morse index of these solutions are given. Also the case λ<λ1 is considered.

scholarly journals Classification of homogeneous bounded domains of lower dimension

1974 ◽  
Vol 53 ◽  
pp. 1-46 ◽  
Author(s):  
Soji Kaneyuki ◽  
Tadashi Tsuji
Keyword(s):  
The Other ◽  
Type I ◽  
Bounded Domains ◽  
Type Ii ◽  
Large Classes ◽  
Siegel Domains ◽  
Dual Cones ◽  
Definition Of ◽  
Lower Dimensional

The theory of classification of homogeneous bounded domains in the complex number space Cn has been developed mainly in the recent papers [10], [6], [3] and [7]. As a result, the classification is reduced to that of S-algebras due to Takeuchi [7] which correspond to irreducible Siegel domains of type I or type II (For the definition of irreducibility see § 1). On the other hand Pjateckii-Sapiro [5] found large classes of homogeneous Siegel domains obtained from classical self-dual cones. Even in lower-dimensional cases, however, there are still homogeneous Siegel domains which do not appear in his results.

scholarly journals The Injectivity Theorem on a Non-Compact Kähler Manifold

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2222
Author(s):  
Jingcao Wu
Keyword(s):  
Sectional Curvature ◽  
Symmetric Spaces ◽  
Kähler Manifold ◽  
Bounded Domains ◽  
Bounded Symmetric Domains ◽  
Curvature Condition ◽  
Kahler Manifold ◽  
Weakly Pseudoconvex ◽  
Compact Kähler Manifold ◽  
Negative Sectional Curvature

In this paper, we establish an injectivity theorem on a weakly pseudoconvex Kähler manifold X with negative sectional curvature. For this purpose, we develop the harmonic theory in this circumstance. The negative sectional curvature condition is usually satisfied by the manifolds with hyperbolicity, such as symmetric spaces, bounded symmetric domains in Cn, hyperconvex bounded domains, and so on.

Interrelations Between the Taylor Coefficients of a Matricial Carathéodory Function and Its Cayley Transform

Analysis ◽  
2005 ◽  
Vol 25 (2) ◽  
Author(s):  
Abdon Eddy Choque Rivero ◽  
Bernd Fritzsche ◽  
Bernd Kirstein
Keyword(s):  
Schur Functions ◽  
The Other ◽  
Schur Function ◽  
Cayley Transform ◽  
Taylor Coefficient ◽  
Explicit Formulas ◽  
Taylor Coefficients ◽  
Carathéodory Functions ◽  
Carathéodory Function ◽  
Q Matrix

AbstractThe main goal of this paper is to discuss several interrelations between the Taylor coefficients of a q x q matrix-valued Carathéodory function and its Cayley transform which is a q x q matrix Schur function. Both Taylor coefficient sequences are described in terms of corresponding matrix balls. Hereby, we will obtain explicit formulas for the parameters of one matrix ball in terms of the other one. These expressions imply a one-to-one correspondence between central matricial Carathéodory functions and central matricial Schur functions which is established via Cayley transform.

scholarly journals UNBOUNDEDNESS OF THE BERGMAN PROJECTIONS ON $L^{p}$ SPACES WITH EXPONENTIAL WEIGHTS

2004 ◽  
Vol 47 (1) ◽  
pp. 111-117 ◽  
Author(s):  
Milutin R. Dostanić
Keyword(s):  
Bergman Projection ◽  
Subject Classification ◽  
Primary 47B10 ◽  
Exponential Weights ◽  
Bergman Projections

AbstractWe prove that the Bergman projection on $L^p(w)$ $(p\neq 2)$, where $w(r)=(1-r^2)^A\textrm{e}^{-B/(1-r^2)^{\alpha}}$, is not bounded.AMS 2000 Mathematics subject classification: Primary 47B10

scholarly journals A note on smoothing properties of the Bergman projection

2016 ◽  
Vol 27 (11) ◽  
pp. 1650087 ◽  
Author(s):  
Sivaguru Ravisankar ◽  
Yunus E. Zeytuncu
Keyword(s):  
Holomorphic Functions ◽  
Bergman Projection ◽  
Bounded Domains ◽  
Satisfy Condition ◽  
Reinhardt Domains ◽  
Smoothing Property

Recently Herbig, McNeal, and Straube have showed that the Bergman projection of conjugate holomorphic functions is smooth up to the boundary on smoothly bounded domains that satisfy condition R. We show that a further smoothing property holds on a family of Reinhardt domains; namely, the Bergman projection of conjugate holomorphic functions is holomorphic past the boundary.

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