reinhardt domain
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2021 ◽  
Vol 71 (4) ◽  
pp. 831-844
Author(s):  
Shuo Zhang

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.


2014 ◽  
Vol 34 (6) ◽  
pp. 1761-1774
Author(s):  
Hongjun LI ◽  
Shuxia FENG

2014 ◽  
Vol 2014 ◽  
pp. 1-15
Author(s):  
Ming-Sheng Liu ◽  
Fengying Yang ◽  
Kit Ian Kou ◽  
Changqin Huang

Some sufficient conditions for biholomorphic convex mappings of orderαon the Reinhardt domainBpninCnare given; from that, criteria for biholomorphic convex mappings of orderαwith particular form become direct. As applications of these sufficient conditions, some concrete biholomorphic convex mappings of orderα  onBpnare provided.


2011 ◽  
Vol 3 (1) ◽  
pp. 31 ◽  
Author(s):  
Z. M. G. Kishka ◽  
M. Saleem ◽  
M. A. Abul-Ez ◽  
H. Abd-Elmageed

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Jianfei Wang ◽  
Cailing Gao

We introduce a new Roper-Suffridge extension operator on the following Reinhardt domaingiven bywherefis a normalized locally biholomorphic function on the unit discD,pjare positive integer,ajare complex constants, andj=2,…,n. Some conditions forajare found under which the operator preserves almost starlike mappings of orderαand starlike mappings of orderα, respectively. In particular, our results reduce to many well-known results when allαj=0.


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