COMPOSITION OPERATORS ON THE LITTLE BLOCH SPACE IN POLYDISCS

2005 ◽  
Vol 25 (4) ◽  
pp. 629-638
Author(s):  
Zehua Zhou ◽  
Min Zhu ◽  
Jihuai Shi
Keyword(s):  
Composition Operators ◽  
Bloch Space ◽  
Little Bloch Space

scholarly journals Linear Combinations of Composition Operators on the Bloch Spaces

2011 ◽  
Vol 63 (4) ◽  
pp. 862-877 ◽  
Author(s):  
Takuya Hosokawa ◽  
Pekka J. Nieminen ◽  
Shûichi Ohno
Keyword(s):  
Composition Operators ◽  
Bloch Space ◽  
Linear Combinations ◽  
Bloch Spaces ◽  
Little Bloch Space

Abstract We characterize the compactness of linear combinations of analytic composition operators on the Bloch space. We also study their boundedness and compactness on the little Bloch space.

scholarly journals Compact composition operators on Block spaces

2003 ◽  
Vol 68 (2) ◽  
pp. 185-190
Author(s):  
Chengji Xiong
Keyword(s):  
Composition Operator ◽  
Composition Operators ◽  
Bloch Space ◽  
Block Spaces ◽  
Little Bloch Space ◽  
New Criteria

The present paper proposes new criteria for compactness of a composition operator Cφf = f ∘ φ on the Bloch space and the little Bloch space. For the case when φ is univalent, a criterion given by K. Madigan and A. Matheson is generalised.

scholarly journals Weighted composition operators on the Bloch space

2001 ◽  
Vol 63 (2) ◽  
pp. 177-185 ◽  
Author(s):  
Shûichi Ohno ◽  
Ruhan Zhao
Keyword(s):  
Composition Operators ◽  
Bloch Space ◽  
Weighted Composition Operators ◽  
Pointwise Multipliers ◽  
Weighted Composition ◽  
Little Bloch Space

We characterise bounded and compact weighted composition operators on the Bloch space and the little Bloch space. The results generalise the known corresponding results on composition operators and pointwise multipliers on the Bloch space and the little Bloch space.

scholarly journals SUMS OF WEIGHTED COMPOSITION OPERATORS ON COP

2012 ◽  
Vol 55 (1) ◽  
pp. 229-239 ◽  
Author(s):  
KEI JI IZUCHI ◽  
KOU HEI IZUCHI ◽  
YUKO IZUCHI
Keyword(s):  
Unit Disk ◽  
Composition Operators ◽  
Bloch Space ◽  
Open Unit ◽  
Weighted Composition Operators ◽  
Open Unit Disk ◽  
Disk Algebra ◽  
Weighted Composition ◽  
Little Bloch Space

AbstractLet COP =0∩H∞, where0is the little Bloch space on the open unit disk, andA() be the disk algebra on. For non-zero functionsu1,u2,. . .,uN∈A() and distinct analytic self-maps ϕ1,ϕ2,. . .,ϕNsatisfying ϕj∈A() and ∥ϕj∥∞=1 for everyj, it is given characterisations of which the sum of weighted composition operators ∑Nj=1ujCϕjmaps COP intoA().

scholarly journals Distance of a Bloch Function to the Little Bloch Space

2006 ◽  
Vol 74 (1) ◽  
pp. 101-119 ◽  
Author(s):  
Maria Tjani
Keyword(s):  
Composition Operators ◽  
Bloch Space ◽  
Essential Norm ◽  
Bloch Function ◽  
Type Spaces ◽  
Little Bloch Space ◽  
Equivalent Expressions

Motivated by a formula of P. Jones that gives the distance of a Bloch function to BMOA, the space of bounded mean oscillations, we obtain several formulas for the distance of a Bloch function to the little Bloch space, β0. Immediate consequences are equivalent expressions for functions in β0. We also give several examples of distances of specific functions to β0. We comment on connections between distance to β0 and the essential norm of some composition operators on the Bloch space, β. Finally we show that the distance formulas in β have Bloch type spaces analogues.

scholarly journals The n-th derivative characterisation of Möbius invariant Dirichlet space

1998 ◽  
Vol 58 (1) ◽  
pp. 43-56 ◽  
Author(s):  
Rauno Aulaskari ◽  
Maria Nowak ◽  
Ruhan Zhao
Keyword(s):  
Carleson Measure ◽  
Bloch Space ◽  
Dirichlet Space ◽  
Function Spaces ◽  
Multiplier Space ◽  
Little Bloch Space ◽  
Special Parameter

In this paper we give the n-th derivative criterion for functions belonging to recently defined function spaces Qp and Qp, 0. For a special parameter value p = 1 this criterion is applied to BMOA and VMOA, and for p > 1 it is applied to the Bloch space and the little Bloch space . Further, a Carleson measure characterisation is given to Qp, and in the last section the multiplier space from Hq into Qp is considered.

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