On Ren-Kähler's Paper "Hardy-Littlewood Inequalities and Qp-Spaces", Z. Anal. Anwendungen 24 (2005), 375 – 388

2007 ◽  
pp. 473-480
Author(s):  
Stevo Stevic
Keyword(s):  
Qp Spaces

Blaschke products in Qp spaces

2000 ◽  
Vol 43 (2) ◽  
pp. 199-209 ◽  
Author(s):  
N. Danikas ◽  
Chr Mouratides
Keyword(s):  
Blaschke Products ◽  
Qp Spaces

Randomization of Qp spaces on the unit ball of ℂn

2005 ◽  
Vol 48 (S1) ◽  
pp. 306-317 ◽  
Author(s):  
Bo Li ◽  
Caiheng Ouyang
Keyword(s):  
Unit Ball ◽  
Qp Spaces

scholarly journals Qp-spaces on bounded symmetric domains

2008 ◽  
Vol 6 (3) ◽  
pp. 205-240 ◽  
Author(s):  
Jonathan Arazy ◽  
Miroslav Engliš
Keyword(s):  
Unit Disc ◽  
Invariant Function ◽  
Function Spaces ◽  
Higher Order ◽  
Bounded Symmetric Domains ◽  
Bloch Spaces ◽  
Qp Spaces

We generalize the theory ofQpspaces, introduced on the unit disc in 1995 by Aulaskari, Xiao and Zhao, to bounded symmetric domains inCd, as well as to analogous Moebius-invariant function spaces and Bloch spaces defined using higher order derivatives; the latter generalization contains new results even in the original context of the unit disc.

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.

Qp Spaces on Riemann Surfaces

1998 ◽  
Vol 50 (3) ◽  
pp. 449-464 ◽  
Author(s):  
Rauno Aulaskari ◽  
Yuzan He ◽  
Juha Ristioja ◽  
Ruhan Zhao
Keyword(s):  
Banach Space ◽  
Riemann Surface ◽  
Unit Disk ◽  
Complex Plane ◽  
Riemann Surfaces ◽  
Bloch Space ◽  
Dirichlet Space ◽  
Function Spaces ◽  
Hyperbolic Riemann Surfaces ◽  
Qp Spaces

AbstractWe study the function spaces Qp(R) defined on a Riemann surface R, which were earlier introduced in the unit disk of the complex plane. The nesting property Qp(R) ⊆Qq(R) for 0 < p < q < ∞ is shown in case of arbitrary hyperbolic Riemann surfaces. Further, it is proved that the classical Dirichlet space AD(R) ⊆ Qp(R) for any p, 0 < p < ∞, thus sharpening T. Metzger's well-known result AD(R) ⊆ BMOA(R). Also the first author's result AD(R) ⊆ VMOA(R) for a regular Riemann surface R is sharpened by showing that, in fact, AD(R) ⊆ Qp,0(R) for all p, 0 < p < ∞. The relationships between Qp(R) and various generalizations of the Bloch space on R are considered. Finally we show that Qp(R) is a Banach space for 0 < p < ∞.

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