Composition Operators from the Hardy Spaces into the Weighted Bloch Spaces on the Polydisc

2009 ◽  
Author(s):  
TaiZhong Zhang ◽  
XiaoFei Yu ◽  
YaPing Cheng
Keyword(s):  
Hardy Spaces ◽  
Composition Operators ◽  
Bloch Spaces

scholarly journals Composition Operators Mapping Logarithmic Bloch Functions into Hardy Space

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
E. G. Kwon
Keyword(s):  
Hardy Space ◽  
Hardy Spaces ◽  
Composition Operators ◽  
Sufficient Conditions ◽  
Hyperbolic Type ◽  
Necessary And Sufficient Conditions ◽  
Bloch Spaces ◽  
Bloch Functions ◽  
Hardy Classes ◽  
Necessary And Sufficient

Characterizing the hyperbolic Hardy classes, several g-functions of hyperbolic type are introduced. Using this, necessary and sufficient conditions on the inducing self-maps are established for the boundedness of the composition operators from logarithmic Bloch spaces into Hardy spaces.

scholarly journals Hardy Spaces for Quasiregular Mappings and Composition Operators

2021 ◽  
Author(s):  
Tomasz Adamowicz ◽  
María J. González
Keyword(s):  
Hardy Spaces ◽  
Composition Operators ◽  
Quasiconformal Mappings ◽  
Carleson Measures ◽  
Quasiregular Mappings ◽  
Classical Setting ◽  
Appl Math ◽  
Analytic Mappings

AbstractWe define Hardy spaces $${\mathcal {H}}^p$$ H p for quasiregular mappings in the plane, and show that for a particular class of these mappings many of the classical properties that hold in the classical setting of analytic mappings still hold. This particular class of quasiregular mappings can be characterised in terms of composition operators when the symbol is quasiconformal. Relations between Carleson measures and Hardy spaces play an important role in the discussion. This program was initiated and developed for Hardy spaces of quasiconformal mappings by Astala and Koskela in 2011 in their paper $${\mathcal {H}}^p$$ H p -theory for Quasiconformal Mappings (Pure Appl Math Q 7(1):19–50, 2011).

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