A Generalized Hilbert Operator on $$\textit{Bloch}$$ Space and $$\textit{BMOA}$$ Spaces

2020 ◽  
pp. 441-449
Author(s):  
S. Naik ◽  
P. K. Nath
Keyword(s):  
Bloch Space ◽  
Bmoa Spaces ◽  
Generalized Hilbert Operator ◽  
Hilbert Operator

scholarly journals Norm and Essential Norm of Composition Followed by Differentiation from Logarithmic Bloch Spaces toHμ∞

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Shanli Ye
Keyword(s):  
Lower Bound ◽  
Unit Disk ◽  
Weighted Space ◽  
Bloch Space ◽  
Essential Norm ◽  
Bloch Spaces

In this note we express the norm of composition followed by differentiationDCφfrom the logarithmic Bloch and the little logarithmic Bloch spaces to the weighted spaceHμ∞on the unit disk and give an upper and a lower bound for the essential norm of this operator from the logarithmic Bloch space toHμ∞.

On Analytic Functions of Bergman BMO in the Ball

1999 ◽  
Vol 42 (1) ◽  
pp. 97-103 ◽  
Author(s):  
E. G. Kwon
Keyword(s):  
Hardy Space ◽  
Composition Operator ◽  
Analytic Functions ◽  
Bloch Space ◽  
Bounded Mean Oscillation ◽  
Open Unit ◽  
Bergman Metric ◽  
Open Unit Ball ◽  
Mean Oscillation ◽  
Volume Measure

AbstractLet B = Bn be the open unit ball of Cn with volume measure v, U = B1 and B be the Bloch space on , 1 ≤ α < 1, is defined as the set of holomorphic f : B → C for whichif 0 < α < 1 and , the Hardy space. Our objective of this note is to characterize, in terms of the Bergman distance, those holomorphic f : B → U for which the composition operator defined by , is bounded. Our result has a corollary that characterize the set of analytic functions of bounded mean oscillation with respect to the Bergman metric.

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