Theory of Np spaces / Le Hai Khoi, Javad Mashreghi.
Khoi, Le Hai.; Mashreghi, Javad.
2023
QA322.2 .K46 2023
Available Online

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Title Theory of Np spaces / Le Hai Khoi, Javad Mashreghi.
Author Khoi, Le Hai.
ISBN 9783031397042 (electronic bk.)
3031397045 (electronic bk.)
3031397037
9783031397035
DOI https://doi.org/10.1007/978-3-031-39704-2
Publication Details Cham : Birkhäuser, 2023.
Language English
Description 1 online resource (261 p.).
Item Number 10.1007/978-3-031-39704-2 doi
Call Number QA322.2 .K46 2023
Dewey Decimal Classification 515/.732
Summary This monograph provides a comprehensive study of a typical and novel function space, known as the $\mathcal{N}_p$ spaces. These spaces are Banach and Hilbert spaces of analytic functions on the open unit disk and open unit ball, and the authors also explore composition operators and weighted composition operators on these spaces. The book covers a significant portion of the recent research on these spaces, making it an invaluable resource for those delving into this rapidly developing area. The authors introduce various weighted spaces, including the classical Hardy space $H^2$, Bergman space $B^2$, and Dirichlet space $\mathcal{D}$. By offering generalized definitions for these spaces, readers are equipped to explore further classes of Banach spaces such as Bloch spaces $\mathcal{B}^p$ and Bergman-type spaces $A^p$. Additionally, the authors extend their analysis beyond the open unit disk $\mathbb{D}$ and open unit ball $\mathbb{B}$ by presenting families of entire functions in the complex plane $\mathbb{C}$ and in higher dimensions. The Theory of $\mathcal{N}_p$ Spaces is an ideal resource for researchers and PhD students studying spaces of analytic functions and operators within these spaces.
Note 11 Np-Type Functions with Hadamard Gaps in the Unit Ball B
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Source of Description Online resource; title from PDF title page (SpringerLink, viewed October 23, 2023).
Added Author Mashreghi, Javad.
Series Frontiers in mathematics.
Available in Other Form Theory of Np Spaces
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Intro
Preface
Contents
1 Function Spaces
1.1 Classical Function Spaces
1.2 Weighted Sequence Spaces
1.3 Special Families of Weighted Sequence Spaces
1.4 Weighted Hardy Spaces
1.5 Special Families of Weighted Hardy Spaces
1.6 Hilbert Spaces of Entire Functions
1.7 Hilbert Spaces of Formal Power Series
1.8 Some Estimations
Notes on Chapter 1
2 The Counting Function and Its Applications
2.1 The Nevanlinna Counting Function
2.2 Littlewood's Inequality
2.3 A Change of Variable Formula
2.4 The Generalized Nevanlinna Counting Function

7.1 On the Unit Ball
7.2 The Automorphism a
7.3 Surjective Isometries
7.4 Np(B) Is a Chain
7.5 The Embedding Np(B)-3mu→A-n+12(B)
7.6 The Embedding A-k(B)-3mu→Np(B)
7.7 Np(B) as a Banach Space
7.8 The Embedding B(B)-3mu→Np(B)
Notes on Chapter 7
8 Weighted Composition Operators on B
8.1 A Test Function
8.2 Boundedness
8.3 Compactness: Easy Reformulations
8.4 Compactness: Characterization
8.5 Estimation of f(z)-f(w)
8.6 Compactness of Difference
8.7 Essential Norm: Upper Bound
8.8 Essential Norm: Lower Bound
Notes on Chapter 8

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