DISTORTION THEORY FOR FUNCTIONS IN A ZYGMUND SPACE Λ

1994 ◽  
Vol 20 (1) ◽  
pp. 18
Author(s):  
Pitt
Keyword(s):  
Zygmund Space

scholarly journals Zygmund inequality of the conjugate function on Morrey-Zygmund spaces

2019 ◽  
Vol 52 (1) ◽  
pp. 97-104
Author(s):  
Tat-Leung Yee ◽  
Kwok-Pun Ho
Keyword(s):  
Unit Circle ◽  
Conjugate Function ◽  
Zygmund Space ◽  
Type Spaces ◽  
Zygmund Spaces

AbstractWe generalize the Zygmund inequality for the conjugate function to the Morrey type spaces defined on the unit circle T. We obtain this extended Zygmund inequality by introducing the Morrey-Zygmund space on T.

scholarly journals Composition Operators on Some Banach Spaces of Harmonic Mappings

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Munirah Aljuaid ◽  
Flavia Colonna
Keyword(s):  
Banach Spaces ◽  
Unit Disk ◽  
Besov Spaces ◽  
Analytic Functions ◽  
Composition Operators ◽  
Harmonic Mappings ◽  
Open Unit ◽  
Open Unit Disk ◽  
Zygmund Space ◽  
Spaces Of Analytic Functions

We study the composition operators on Banach spaces of harmonic mappings that extend several well-known Banach spaces of analytic functions on the open unit disk in the complex plane, including the α-Bloch spaces, the growth spaces, the Zygmund space, the analytic Besov spaces, and the space BMOA.

scholarly journals Isometries and Hermitian Operators on Zygmund Spaces

2015 ◽  
Vol 58 (2) ◽  
pp. 241-249 ◽  
Author(s):  
Fernanda Botelho
Keyword(s):  
Integral Operators ◽  
Zygmund Space ◽  
Zygmund Spaces

AbstractIn this paper we characterize the isometries of subspaces of the little Zygmund space. We show that the isometries of these spaces are surjective and represented as integral operators. We also show that all hermitian operators on these settings are bounded

scholarly journals Weighted Composition Operators from the Bloch Space and the Analytic Besov Spaces into the Zygmund Space

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Flavia Colonna ◽  
Songxiao Li
Keyword(s):  
Composition Operator ◽  
Besov Spaces ◽  
Composition Operators ◽  
Bloch Space ◽  
Weighted Composition Operators ◽  
Zygmund Space ◽  
Weighted Composition ◽  
Special Case

We provide several characterizations of the bounded and the compact weighted composition operators from the Bloch space and the analytic Besov spaces (with ) into the Zygmund space . As a special case, we show that the bounded (resp., compact) composition operators from , , and to coincide. In addition, the boundedness and the compactness of the composition operator can be characterized in terms of the boundedness (resp., convergence to 0, under the boundedness assumption of the operator) of the Zygmund norm of the powers of the symbol.

ON THE HARMONIC ZYGMUND SPACES

2020 ◽  
Vol 101 (3) ◽  
pp. 466-476
Author(s):  
MUNIRAH ALJUAID ◽  
FLAVIA COLONNA
Keyword(s):  
Unit Disk ◽  
Complex Plane ◽  
Harmonic Mappings ◽  
Open Unit ◽  
Open Unit Disk ◽  
Zygmund Space ◽  
Class A ◽  
Analytic Case ◽  
Separable Subspace ◽  
Zygmund Spaces

In this paper we study a class ${\mathcal{Z}}_{H}$ of harmonic mappings on the open unit disk $\mathbb{D}$ in the complex plane that is an extension of the classical (analytic) Zygmund space. We extend to the elements of this class a characterisation that is valid in the analytic case. We also provide a similar result for a closed separable subspace of ${\mathcal{Z}}_{H}$ which we call the little harmonic Zygmund space.

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