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E-raamat: Mobius Invariant QK Spaces

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  • Formaat: EPUB+DRM
  • Ilmumisaeg: 03-Jul-2017
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319582870
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Mobius Invariant QK SpacesSuurem pilt
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 03-Jul-2017
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319582870
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This monograph summarizes the recent major achievements in Möbius invariant QK spaces. First introduced by Hasi Wulan and his collaborators, the theory of QK spaces has developed immensely in the last two decades, and the topics covered in this book will be helpful to graduate students and new researchers interested in the field. Featuring a wide range of subjects, including an overview of QK spaces, QK-Teichmüller spaces, K-Carleson measures and analysis of weight functions, this book serves as an important resource for analysts interested in this area of complex analysis. Notes, numerous exercises, and a comprehensive up-to-date bibliography provide an accessible entry to anyone with a standard graduate background in real and complex analysis.

Arvustused

The book has a comprehensive and up-to-date bibliography, which is a valuable asset to any researcher in the field. Without a question, the book under review is useful for the student contemplating working in the field. I am also happy to notice that the book has something to offer for researchers at all levels, as it is a thorough and illuminating presentation of the current state of the theory. (Janne Gröhn, Mathematical Reviews, March, 2018)

This comprehensive monograph summarizes the main results about QK spaces obtained since the beginning of this century. It is reader-friendly, well written, self-contained and well structured. this book will be useful to researchers interested in this field under active development. Moreover, each chapter ends with a list of exercises and it would be an excellent textbook for advanced students with a good background in real and complex analysis. (Joan Fàbrega, zbMATH 1387.30001, 2018)

1 Mobius Invariant Function Spaces
1(24)
1.1 The Mobius Group
1(3)
1.2 Mobius Invariant Function Spaces
4(4)
1.3 General Properties
8(8)
1.4 Uniqueness of the Dirichlet Space
16(2)
1.5 The Invariant Dual
18(4)
1.6 Notes
22(1)
1.7 Exercises
22(3)
2 QK Spaces
25(34)
2.1 Preliminaries
25(5)
2.2 The Definition of QK
30(6)
2.3 The Subspace QK.0
36(5)
2.4 Comparing Two QK Spaces
41(5)
2.5 Examples of Functions in QK
46(10)
2.6 Notes
56(1)
2.7 Exercises
57(2)
3 Analysis of Weight Functions
59(22)
3.1 Standing Assumptions
59(1)
3.2 Modifications of the Weight Function
60(8)
3.3 Integral Estimates
68(11)
3.4 Notes
79(1)
3.5 Exercises
79(2)
4 K-Carleson Measures
81(38)
4.1 QK-Carleson Measures
81(12)
4.2 QK Spaces via Carleson Measures
93(3)
4.3 Inner Functions in QK
96(9)
4.4 Outer Functions in QK
105(5)
4.5 Boundary QK Spaces
110(5)
4.6 Notes
115(1)
4.7 Exercises
116(3)
5 QK Spaces via Other Derivatives
119(24)
5.1 Raising the Order of Derivative
119(4)
5.2 Lowering the Order of Derivative
123(3)
5.3 Another Approach to Higher Order Derivatives
126(5)
5.4 QK Spaces via Fractional Order Derivatives
131(2)
5.5 Derivative-Free Characterizations
133(7)
5.6 Notes
140(1)
5.7 Exercises
141(2)
6 Taylor Series and QK Spaces
143(20)
6.1 Lacunary Series in QK
143(8)
6.2 Mean Lipschitz Spaces and QK
151(4)
6.3 Hadamard Products
155(5)
6.4 Notes
160(1)
6.5 Exercises
160(3)
7 Decompositions and Interpolation
163(26)
7.1 Preliminaries
163(6)
7.2 Atomic Decomposition for QK
169(6)
7.3 Atomic Decomposition for QK.0
175(1)
7.4 A Fefferman-Stein Decomposition
176(2)
7.5 Interpolation in Spaces
178(9)
7.6 Notes
187(1)
7.7 Exercises
187(2)
8 QK-Teichmuller Spaces
189(30)
8.1 Carleson Measures on C \ D
189(4)
8.2 QK-Teichmuller Spaces
193(4)
8.3 The Schwarzian Derivative and QK Spaces
197(8)
8.4 Geometric Descriptions of QK.0 Spaces
205(6)
8.5 K and QK
211(5)
8.6 Notes
216(1)
8.7 Exercises
216(3)
9 Additional Topics
219(32)
9.1 Preduals of QK Spaces
219(5)
9.2 Morrey K-Spaces
224(7)
9.3 The Corona Problem for QK
231(1)
9.4 Distances from Bloch Functions to QK Spaces
232(6)
9.5 Korenblum's Inequality for QK
238(4)
9.6 Notes
242(1)
9.7 Exercises
242(9)
References
245(6)
Index 251
Hasi Wulan is a professor, Ph.D supervisor, and the current Vice President of Shantou University. His research areas are function spaces and theory of operators as well as holomorphic functions of one and several complex variables. Kehe Zhu is a professor in the Department of Mathematics and Statistics at the State University of New York at Albany. His research interests include operators on holomorphic function spaces, complex analysis, and operator theory and operator algebras.
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