Dirichlet and Bergman Spaces of Holomorphic Functions on the Unit Ball of ?n

2005 ◽  
Vol 144 (2) ◽  
pp. 131-139
Author(s):  
Manfred Stoll
Keyword(s):  
Unit Ball ◽  
Bergman Spaces ◽  
Holomorphic Functions ◽  
Spaces Of Holomorphic Functions

Holomorphic Functions with Positive Real Part

1982 ◽  
Vol 34 (1) ◽  
pp. 1-7 ◽  
Author(s):  
Eric Sawyer
Keyword(s):  
Unit Ball ◽  
Hardy Spaces ◽  
Convex Cone ◽  
Holomorphic Functions ◽  
Positive Real Part ◽  
Positive Real ◽  
Spaces Of Holomorphic Functions ◽  
Extreme Element ◽  
Image Position ◽  
Special Case

The main purpose of this note is to prove a special case of the following conjecture.Conjecture. If F is holomorphic on the unit ball Bn in Cn and has positive real part, then F is in Hp(Bn) for 0 < p < ½(n + 1).Here Hp(Bn) (0 < p < ∞) denote the usual Hardy spaces of holomorphic functions on Bn. See below for definitions. We remark that the conjecture is known for 0 < p < 1 and that some evidence for it already exists in the literature; for example [1, Theorems 3.11 and 3.15] where it is shown that a particular extreme element of the convex cone of functionsis in Hp(B2) for 0 < p < 3/2.

On Classes for Hyperbolic Riemann Surfaces

2016 ◽  
Vol 59 (01) ◽  
pp. 13-29
Author(s):  
Rauno Aulaskari ◽  
Huaihui Chen
Keyword(s):  
Unit Ball ◽  
Riemann Surfaces ◽  
Meromorphic Functions ◽  
Holomorphic Functions ◽  
Spaces Of Holomorphic Functions ◽  
Inclusion Relations ◽  
Hyperbolic Riemann Surfaces ◽  
Qp Spaces

AbstractThe Qpspaces of holomorphic functions on the disk, hyperbolic Riemann surfaces or complex unit ball have been studied deeply. Meanwhile, there are a lot of papers devoted to theclasses of meromorphic functions on the disk or hyperbolic Riemann surfaces. In this paper, we prove the nesting property (inclusion relations) ofclasses on hyperbolic Riemann surfaces. The same property for Qp spaces was also established systematically and precisely in earlier work by the authors of this paper.

scholarly journals Holomorphic Spaces in the Unit Ball of

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Augusto Guadalupe Miss Paredes ◽  
Lino Feliciano Reséndis Ocampo ◽  
Luis Manuel Tovar Sánchez
Keyword(s):  
Unit Ball ◽  
Holomorphic Functions ◽  
Vector Spaces ◽  
Spaces Of Holomorphic Functions ◽  
Harmonic Majorants

We introduce the and vector spaces of holomorphic functions defined in the unit ball of , generalizing previous work like Ouyang et al. (1998), Stroethoff (1989), and Choa et al. (1992). Likewise, we characterize those spaces in terms of harmonic majorants as a generalization of Arellano et al. (2000).

scholarly journals Weighted Iterated Radial Composition Operators between Some Spaces of Holomorphic Functions on the Unit Ball

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Stevo Stević
Keyword(s):  
Unit Ball ◽  
Composition Operators ◽  
Holomorphic Functions ◽  
Mixed Norm ◽  
Mixed Norm Space ◽  
Type Space ◽  
Spaces Of Holomorphic Functions ◽  
Schmidt Norm ◽  
Norm Space ◽  
Weighted Type

The boundedness and compactness of weighted iterated radial composition operators from the mixed-norm space to the weighted-type space and the little weighted-type space on the unit ball are characterized here. We also calculate the Hilbert-Schmidt norm of the operator on the weighted Bergman-Hilbert space as well as on the Hardy space.

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