Weighted Composition Operators from H ∞ to the Bloch Space of a Bounded Homogeneous Domain

2010 ◽  
Vol 66 (1) ◽  
pp. 21-40 ◽  
Author(s):  
Robert F. Allen ◽  
Flavia Colonna
Keyword(s):  
Composition Operators ◽  
Bloch Space ◽  
Weighted Composition Operators ◽  
Homogeneous Domain ◽  
Weighted Composition ◽  
Bounded Homogeneous Domain

scholarly journals Weighted Composition Operators from Hardy Spaces into Logarithmic Bloch Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Flavia Colonna ◽  
Songxiao Li
Keyword(s):  
Banach Space ◽  
Hardy Spaces ◽  
Composition Operators ◽  
Bloch Space ◽  
Weighted Composition Operator ◽  
Open Unit ◽  
Weighted Composition Operators ◽  
Open Unit Disk ◽  
Space Of Analytic Functions ◽  
Weighted Composition

The logarithmic Bloch spaceBlog⁡is the Banach space of analytic functions on the open unit disk&#x1D53B;whose elementsfsatisfy the condition∥f∥=sup⁡z∈&#x1D53B;(1-|z|2)log⁡  (2/(1-|z|2))|f'(z)|<∞. In this work we characterize the bounded and the compact weighted composition operators from the Hardy spaceHp(with1≤p≤∞) into the logarithmic Bloch space. We also provide boundedness and compactness criteria for the weighted composition operator mappingHpinto the little logarithmic Bloch space defined as the subspace ofBlog⁡consisting of the functionsfsuch thatlim⁡|z|→1(1-|z|2)log⁡  (2/(1-|z|2))|f'(z)|=0.

scholarly journals ISOMETRIES AND SPECTRA OF MULTIPLICATION OPERATORS ON THE BLOCH SPACE

2009 ◽  
Vol 79 (1) ◽  
pp. 147-160 ◽  
Author(s):  
ROBERT F. ALLEN ◽  
FLAVIA COLONNA
Keyword(s):  
Unit Disk ◽  
Composition Operators ◽  
Bloch Space ◽  
Multiplication Operators ◽  
Weighted Composition Operators ◽  
Weighted Composition

AbstractIn this paper, we establish bounds on the norm of multiplication operators on the Bloch space of the unit disk via weighted composition operators. In doing so, we characterize the isometric multiplication operators to be precisely those induced by constant functions of modulus 1. We then describe the spectrum of the multiplication operators in terms of the range of the symbol. Lastly, we identify the isometries and spectra of a particular class of weighted composition operators on the Bloch space.

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