Möbius-Invariant Harmonic Function Spaces on the Unit Disc

2021 ◽  
Author(s):  
H. T. Kaptanoğlu ◽  
A. E. Üreyen
Keyword(s):  
Harmonic Function ◽  
Unit Disc ◽  
Function Spaces

scholarly journals A note on n-harmonic majorants

1986 ◽  
Vol 34 (3) ◽  
pp. 461-472
Author(s):  
Hong Oh Kim ◽  
Chang Ock Lee
Keyword(s):  
Harmonic Function ◽  
Complex Plane ◽  
Unit Disc ◽  
Dirichlet Integral ◽  
Harmonic Majorant ◽  
Harmonic Majorants

Suppose D (υ) is the Dirichlet integral of a function υ defined on the unit disc U in the complex plane. It is well known that if υ is a harmonic function in U with D (υ) < ∞, then for each p, 0 < p < ∞, |υ|p has a harmonic majorant in U.We define the “iterated” Dirichlet integral Dn (υ) for a function υ on the polydisc Un of Cn and prove the polydisc version of the well known fact above:If υ is an n-harmonic function in Un with Dn (υ) < ∞, then for each p, 0 < p < ∞, |υ|p has an n-harmonic majorant in Un.

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.

HARMONIC FUNCTION SPACES ON GROUPS

2004 ◽  
Vol 70 (01) ◽  
pp. 182-198 ◽  
Author(s):  
CHO-HO CHU
Keyword(s):  
Harmonic Function ◽  
Function Spaces

scholarly journals Norm of a Volterra Integral Operator on Some Analytic Function Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Hao Li ◽  
Songxiao Li
Keyword(s):  
Analytic Function ◽  
Integral Operator ◽  
Unit Disc ◽  
Function Spaces ◽  
Volterra Integral Operator ◽  
Analytic Function Spaces

Let f be an analytic function in the unit disc 𝔻. The Volterra integral operator If is defined as follows: If(h)(z)=∫0zf(w)h'(w)dw,h∈H(𝔻),z∈𝔻. In this paper, we compute the norm of If on some analytic function spaces.

scholarly journals On the Existence of Radial Limits

2014 ◽  
Vol 58 (1) ◽  
pp. 47-51
Author(s):  
Martha Guzmán-Partida ◽  
Carlos Robles-Corbala
Keyword(s):  
Harmonic Function ◽  
Unit Disc ◽  
Harmonic Functions ◽  
Radial Limits

Abstract We discuss conditions that ensure the existence of radial limits a.e. for harmonic functions defined on the unit disc D. We give an example of a Banach-valued harmonic function without radial limits at almost every point on the boundary of D.

scholarly journals Eigenvalue decay of operators on harmonic function spaces

2009 ◽  
Vol 41 (5) ◽  
pp. 903-915 ◽  
Author(s):  
Oscar F. Bandtlow ◽  
Cho-Ho Chu
Keyword(s):  
Harmonic Function ◽  
Function Spaces

Mean Growth of Harmonic Functions of Beurling Type

1984 ◽  
Vol 27 (4) ◽  
pp. 405-409
Author(s):  
Manning G. Collier ◽  
John A. Kelingos
Keyword(s):  
Growth Rate ◽  
Harmonic Function ◽  
General Result ◽  
Unit Disc ◽  
Harmonic Functions ◽  
Concave Function ◽  
Taylor Coefficients

AbstractA harmonic function on the unit disc is of Beurling type ω if its Fourier (or Taylor) coefficients grow no faster than exp ω(|n|) as |n|→∞, where ω is a given increasing, concave function with ω(x)/x ↓ 0 as x → ∞. These harmonic functions are characterized by the growth rate of their L1-norms on circles of radius r as r → 1. The classical Schwartz result follows as a corollary by taking ω(x) = log(1+x). The Gevrey case is also included in the general result if one uses ω(x) = xα, 0 < α < 1.

scholarly journals On harmonic function spaces

2005 ◽  
Vol 57 (3) ◽  
pp. 781-802 ◽  
Author(s):  
Stevo STEVIĆ
Keyword(s):  
Harmonic Function ◽  
Function Spaces
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