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.

scholarly journals On Hardy spaces on worm domains

2016 ◽  
Vol 3 (1) ◽  
Author(s):  
Alessandro Monguzzi
Keyword(s):  
Sobolev Spaces ◽  
Hardy Spaces ◽  
Pseudoconvex Domain ◽  
Bergman Projection ◽  
Review Article ◽  
High Order ◽  
Worm Domains

AbstractIn this review article we present the problem of studying Hardy spaces and the related Szeg˝o projection on worm domains. We review the importance of the Diederich–Fornæss worm domain as a smooth bounded pseudoconvex domain whose Bergman projection does not preserve Sobolev spaces of sufficiently high order and we highlight which difficulties arise in studying the same problem for the Szeg˝o projection. Finally, we announce and discuss the results we have obtained so far in the setting of non-smooth worm domains.

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 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 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.

scholarly journals Logarithmically Convex Reinhardt Domains

2003 ◽  
Vol 25 (25) ◽  
pp. 07 ◽  
Author(s):  
Ludmila Bourchtein ◽  
Andrei Bourchtein
Keyword(s):  
Power Series ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Reinhardt Domain ◽  
Reinhardt Domains ◽  
Logarithmic Convexity

The domains of certain types, such as Reinhardt ones, are important in different problems of theory of functions of several complex variables. For instance, any power series of several complex variables converges in the complete logarithmically convex Reinhardt domain. In this article we prove the logarithmic convexity of complete convex Reinhardt domain.

scholarly journals Bicomplex Bergman and Bloch spaces

2020 ◽  
Vol 9 (3) ◽  
pp. 665-679
Author(s):  
L. F. Reséndis O. ◽  
L. M. Tovar S.
Keyword(s):  
Bloch Space ◽  
Bergman Spaces ◽  
Bergman Projection ◽  
Weighted Bergman Spaces ◽  
Bergman Kernels ◽  
Bloch Spaces ◽  
Bergman Projections

Abstract In this article, we define the bicomplex weighted Bergman spaces on the bidisk and their associated weighted Bergman projections, where the respective Bergman kernels are determined. We study also the bicomplex Bergman projection onto the bicomplex Bloch space.

Multi-index drought characteristics in Songhua River basin, Northeast China

2019 ◽  
Vol 78 (1) ◽  
pp. 1-19 ◽  
Author(s):  
MA Faiz ◽  
D Liu ◽  
Q Fu ◽  
F Baig ◽  
AA Tahir ◽  
...  
Keyword(s):  
River Basin ◽  
Northeast China ◽  
Songhua River ◽  
Multi Index ◽  
Songhua River Basin ◽  
Drought Characteristics
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