scholarly journals On Distance Function in Some New Analytic Bergman Type Spaces inℂn

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Romi F. Shamoyan ◽  
Olivera R. Mihić
Keyword(s):  
Unit Disk ◽  
Distance Function ◽  
Harmonic Functions ◽  
Higher Dimensions ◽  
Mixed Norm ◽  
Type Spaces

We extend our previous sharp results on distances obtained for analytic Bergman type spaces in unit disk to some new analytic Bergman type spaces in higher dimensions inℂn. Also, we study the same problem in anisotropic mixed normh(p,q,s)spaces consisting ofn-harmonic functions on the unit polydisc ofℂn.

scholarly journals Random Harmonic Functions in Growth Spaces and Bloch-type Spaces

2014 ◽  
Vol 66 (2) ◽  
pp. 284-302
Author(s):  
Kjersti Solberg Eikrem
Keyword(s):  
Unit Ball ◽  
Unit Disk ◽  
Spherical Harmonics ◽  
Harmonic Functions ◽  
Higher Dimensions ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Doubling Condition ◽  
Similar Characterization ◽  
Type Spaces

Abstract. Let h∞v (D) and h∞v (B) be the spaces of harmonic functions in the unit disk and multidimensional unit ball admitting a two-sided radial majorant v(r). We consider functions v that fulfill a doubling condition. In the two-dimensional case letwhere ξ ={ξji} is a sequence of random subnormal variables and aji are real. In higher dimensions we consider series of spherical harmonics. We will obtain conditions on the coefficients aji that imply that u is in h∞v (B) almost surely. Our estimate improves previous results by Bennett, Stegenga, and Timoney, and we prove that the estimate is sharp. The results for growth spaces can easily be applied to Bloch-type spaces, and we obtain a similar characterization for these spaces that generalizes results by Anderson, Clunie, and Pommerenke and by Guo and Liu.

scholarly journals Harmonic Functions Starlike in the Unit Disk

1999 ◽  
Vol 235 (2) ◽  
pp. 470-477 ◽  
Author(s):  
Jay M Jahangiri
Keyword(s):  
Unit Disk ◽  
Harmonic Functions

scholarly journals Bloch-Type Spaces of Minimal Surfaces

2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Guanghua He ◽  
Xi Fu ◽  
Hancan Zhu
Keyword(s):  
Unit Disk ◽  
Composition Operator ◽  
Minimal Surfaces ◽  
Lipschitz Functions ◽  
Type Spaces

We study Bloch-type spaces of minimal surfaces from the unit disk D into Rn and characterize them in terms of weighted Lipschitz functions. In addition, the boundedness of a composition operator Cϕ acting between two Bloch-type spaces is discussed.

scholarly journals The Multiplication Operator fromF(p,q,s)Spaces tonth Weighted-Type Spaces on the Unit Disk

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Yongmin Liu ◽  
Yanyan Yu
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Multiplication Operator ◽  
Space Of Analytic Functions ◽  
Type Spaces ◽  
Weighted Type

LetH(𝔻)be the space of analytic functions on𝔻andu∈H(𝔻). The boundedness and compactness of the multiplication operatorMufromF(p,q,s),(or  F0(p,q,s))spaces tonth weighted-type spaces on the unit disk are investigated in this paper.

scholarly journals On an Integral-Type Operator from Zygmund-Type Spaces to Mixed-Norm Spaces on the Unit Ball

2010 ◽  
Vol 2010 ◽  
pp. 1-7 ◽  
Author(s):  
Stevo Stević
Keyword(s):  
Unit Ball ◽  
Type Operator ◽  
Mixed Norm ◽  
Integral Type ◽  
Mixed Norm Space ◽  
Mixed Norm Spaces ◽  
Norm Space ◽  
Type Spaces

The boundedness and compactness of an integral-type operator recently introduced by the author from Zygmund-type spaces to the mixed-norm space on the unit ball are characterized here.

Bergman Type Spaces on the Unit Disk

2001 ◽  
pp. 399-409 ◽  
Author(s):  
Nikolai Vasilevski
Keyword(s):  
Unit Disk ◽  
Type Spaces

A Maximum Principle for Dirichlet-Finite Harmonic Functions on Riemannian Spaces

1970 ◽  
Vol 22 (4) ◽  
pp. 855-862
Author(s):  
Y. K. Kwon ◽  
L. Sario
Keyword(s):  
Maximum Principle ◽  
Harmonic Functions ◽  
Riemann Surfaces ◽  
Decomposition Theorem ◽  
Higher Dimensions ◽  
Integral Representations ◽  
Classification Theory ◽  
Topological Properties ◽  
Harmonic Decomposition ◽  
Bounded Harmonic Functions

Representations of harmonic functions by means of integrals taken over the harmonic boundary ΔR of a Riemann surface R enable one to study the classification theory of Riemann surfaces in terms of topological properties of ΔR (cf. [6; 4; 1; 7]). In deducing such integral representations, essential use is made of the fact that the functions in question attain their maxima and minima on ΔR.The corresponding maximum principle in higher dimensions was discussed for bounded harmonic functions in [3]. In the present paper we consider Dirichlet-finite harmonic functions. We shall show that every such function on a subregion G of a Riemannian N-space R attains its maximum and minimum on the set , where ∂G is the relative boundary of G in R and the closures are taken in Royden's compactification R*. As an application we obtain the harmonic decomposition theorem relative to a compact subset K of R* with a smooth ∂(K ∩ R).

scholarly journals On Extremal Problems in Certain New Bergman Type Spaces in Some Bounded Domains inCn

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Romi F. Shamoyan ◽  
Olivera Mihić
Keyword(s):  
Unit Disk ◽  
Bergman Kernel ◽  
Extremal Problems ◽  
Bergman Projection ◽  
Bounded Domains ◽  
Bounded Symmetric Domains ◽  
Siegel Domains ◽  
Type Spaces ◽  
Tube Type ◽  
Homogeneous Domains

Based on recent results on boundedness of Bergman projection with positive Bergman kernel in analytic spaces in various types of domains inCn, we extend our previous sharp results on distances obtained for analytic Bergman type spaces in unit disk to some new Bergman type spaces in Lie ball, bounded symmetric domains of tube type, Siegel domains, and minimal bounded homogeneous domains.

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