scholarly journals Composition operators on Hardy-Sobolev spaces and BMO-quasiconformal mappings

2021 ◽  
Vol 18 (2) ◽  
pp. 209-225
Author(s):  
Alexander Menovschikov ◽  
Alexander Ukhlov
Keyword(s):  
Sobolev Spaces ◽  
Hardy Spaces ◽  
Composition Operators ◽  
Quasiconformal Mappings ◽  
Bmo Spaces

In this paper, we consider composition operators on Hardy-Sobolev spaces in connections with $\BMO$-quasiconformal mappings. Using the duality of Hardy spaces and $\BMO$-spaces, we prove that $\BMO$-quasiconformal mappings generate bounded composition operators from Hardy--Sobolev spaces to Sobolev 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).

Weak compactness of Fréchet-derivatives: application to composition operators

1980 ◽  
Vol 29 (4) ◽  
pp. 399-406
Author(s):  
Peter Dierolf ◽  
Jürgen Voigt
Keyword(s):  
Banach Spaces ◽  
Integral Equations ◽  
Sobolev Spaces ◽  
Composition Operators ◽  
Weak Compactness ◽  
Nonlinear Integral Equations ◽  
Weakly Compact ◽  
Frechet Derivatives ◽  
Fréchet Derivatives ◽  
Compact Map

AbstractWe prove a result on compactness properties of Fréchet-derivatives which implies that the Fréchet-derivative of a weakly compact map between Banach spaces is weakly compact. This result is applied to characterize certain weakly compact composition operators on Sobolev spaces which have application in the theory of nonlinear integral equations and in the calculus of variations.

Sobolev spaces and (P,Q)-quasiconformal mappings of carnot groups

1998 ◽  
Vol 39 (4) ◽  
pp. 665-682 ◽  
Author(s):  
S. K. Vodop'yanov ◽  
A. D. Ukhlov
Keyword(s):  
Sobolev Spaces ◽  
Quasiconformal Mappings ◽  
Carnot Groups

Linear Combinations of Composition Operators on the Fock-Sobolev Spaces

2014 ◽  
Vol 41 (4) ◽  
pp. 1223-1246 ◽  
Author(s):  
Hong Rae Cho ◽  
Boo Rim Choe ◽  
Hyungwoon Koo
Keyword(s):  
Sobolev Spaces ◽  
Composition Operators ◽  
Linear Combinations
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