The Diagonal Mapping in Bmoa-Type Spaces of Analytic Functions on the Polydisk

2009 ◽  
Vol 16 (3) ◽  
pp. 561-574
Author(s):  
Romi F. Shamoyan
Keyword(s):  
Holomorphic Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Unit Disc ◽  
Diagonal Mapping ◽  
Type Spaces ◽  
Unit Polydisk ◽  
Spaces Of Analytic Functions

Abstract For any holomorphic function 𝑓 on the unit polydisk we consider its restriction to the diagonal, i.e., the function in the unit disc 𝔻 ⊂ ℂ defined by Diag 𝑓(𝑧) = 𝑓(𝑧, . . . , 𝑧) and prove that the diagonal map Diag maps the space of the polydisk onto the space of the unit disk.

scholarly journals QKtype spaces of analytic functions

2006 ◽  
Vol 4 (1) ◽  
pp. 73-84 ◽  
Author(s):  
Hasi Wulan ◽  
Jizhen Zhou
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Nondecreasing Function ◽  
Necessary And Sufficient Conditions ◽  
Type Space ◽  
Necessary And Sufficient ◽  
Spaces Of Analytic Functions

For a nondecreasing functionK:[0,8)?[0,8)and0<p<8,-2<q<8, we introduceQK(p,q), aQKtype space of functions analytic in the unit disk and study the characterizations ofQK(p,q). Necessary and sufficient conditions onKsuch thatQK(p,q)become some known spaces are given.

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(&#x1D53B;)be the space of analytic functions on&#x1D53B;andu∈H(&#x1D53B;). 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 Area Nevanlinna Type Classes of Analytic Functions in the Unit Disk and Related Spaces

2018 ◽  
Vol 26 (1) ◽  
pp. 47-76
Author(s):  
Romi Shamoyan ◽  
Seraphim Maksakov
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Zero Sets ◽  
Recent Advances ◽  
Type Classes ◽  
Spaces Of Analytic Functions

Abstract The survey collects many recent advances on area Nevanlinna type classes and related spaces of analytic functions in the unit disk concern- ing zero sets and factorization representations of these classes and discusses approaches, used in proofs of these results.

scholarly journals The Bloch space and Besov spaces of analytic functions

1996 ◽  
Vol 54 (2) ◽  
pp. 211-219 ◽  
Author(s):  
Karel Stroethoff
Keyword(s):  
Unit Disk ◽  
Complex Plane ◽  
Besov Spaces ◽  
Analytic Functions ◽  
Elementary Proof ◽  
Bloch Space ◽  
Little Bloch Space ◽  
Spaces Of Analytic Functions

We shall give an elementary proof of a characterisation for the Bloch space due to Holland and Walsh, and obtain analogous characterisations for the little Bloch space and Besov spaces of analytic functions on the unit disk in the complex plane.

Invariant subspaces of given index in Banach spaces of analytic functions

1998 ◽  
Vol 1998 (505) ◽  
pp. 23-44 ◽  
Author(s):  
Alexander Borichev
Keyword(s):  
Banach Spaces ◽  
Wide Class ◽  
Analytic Functions ◽  
Unit Disc ◽  
Bergman Spaces ◽  
Invariant Subspaces ◽  
Weighted Bergman Spaces ◽  
Common Zeros ◽  
Spaces Of Analytic Functions

Abstract For a wide class of Banach spaces of analytic functions in the unit disc including all weighted Bergman spaces with radial weights and for weighted ℓAp spaces we construct z-invariant subspaces of index n, 2 ≦ n ≦ + ∞, without common zeros in the unit disc.

scholarly journals On M-ideals and o-O type spaces

2017 ◽  
Vol 121 (1) ◽  
pp. 151 ◽  
Author(s):  
Karl-Mikael Perfekt
Keyword(s):  
Banach Spaces ◽  
Analytic Functions ◽  
Function Spaces ◽  
Weighted Spaces ◽  
Bounded Mean Oscillation ◽  
Mean Oscillation ◽  
Type Spaces ◽  
Invariant Spaces ◽  
Holder Spaces ◽  
Spaces Of Analytic Functions

We consider pairs of Banach spaces $(M_0, M)$ such that $M_0$ is defined in terms of a little-$o$ condition, and $M$ is defined by the corresponding big-$O$ condition. The construction is general and pairs include function spaces of vanishing and bounded mean oscillation, vanishing weighted and weighted spaces of functions or their derivatives, Möbius invariant spaces of analytic functions, Lipschitz-Hölder spaces, etc. It has previously been shown that the bidual $M_0^{**}$ of $M_0$ is isometrically isomorphic with $M$. The main result of this paper is that $M_0$ is an M-ideal in $M$. This has several useful consequences: $M_0$ has Pełczýnskis properties (u) and (V), $M_0$ is proximinal in $M$, and $M_0^*$ is a strongly unique predual of $M$, while $M_0$ itself never is a strongly unique predual.

scholarly journals Majorization Results for Certain Subfamilies of Analytic Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Muhammad Arif ◽  
Miraj Ul-Haq ◽  
Omar Barukab ◽  
Sher Afzal Khan ◽  
Saleem Abullah
Keyword(s):  
Holomorphic Function ◽  
Analytic Functions ◽  
Unit Disc ◽  
Holomorphic Functions ◽  
Open Unit ◽  
Open Unit Disc

Let h 1 z and h 2 z be two nonvanishing holomorphic functions in the open unit disc with h 1 0 = h 2 0 = 1 . For some holomorphic function q z , we consider the class consisting of normalized holomorphic functions f whose ratios f z / z q z and q z are subordinate to h 1 z and h 2 z , respectively. The majorization results are obtained for this class when h 1 z is chosen either h 1 z = cos z or h 1 z = 1 + sin z or h 1 z = 1 + z and h 2 z = 1 + sin z .

scholarly journals Composition Operators on Some Banach Spaces of Harmonic Mappings

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Munirah Aljuaid ◽  
Flavia Colonna
Keyword(s):  
Banach Spaces ◽  
Unit Disk ◽  
Besov Spaces ◽  
Analytic Functions ◽  
Composition Operators ◽  
Harmonic Mappings ◽  
Open Unit ◽  
Open Unit Disk ◽  
Zygmund Space ◽  
Spaces Of Analytic Functions

We study the composition operators on Banach spaces of harmonic mappings that extend several well-known Banach spaces of analytic functions on the open unit disk in the complex plane, including the α-Bloch spaces, the growth spaces, the Zygmund space, the analytic Besov spaces, and the space BMOA.

scholarly journals Monomial basis in Korenblum type spaces of analytic functions

2018 ◽  
Vol 146 (12) ◽  
pp. 5269-5278 ◽  
Author(s):  
José Bonet ◽  
Wolfgang Lusky ◽  
Jari Taskinen
Keyword(s):  
Analytic Functions ◽  
Monomial Basis ◽  
Type Spaces ◽  
Spaces Of Analytic Functions
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