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- Quick and concise introduction to several important classical topics of real analysis Exposition of powerful results of recent research in a self-contained manner, making them accessible to beginners Presents results not yet available in existing literature Contains descriptions of new techniques which may be useful in other research problems ?
- Includes supplementary material: sn.pub/extras
Part of the book series: Monografie Matematyczne (MONOGRAFIE, volume 74)
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Table of contents (11 chapters)
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Front Matter
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Advanced theory
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Front Matter
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Back Matter
About this book
In this book we suggest a unified method of constructing near-minimizers for certain important functionals arising in approximation, harmonic analysis and ill-posed problems and most widely used in interpolation theory. The constructions are based on far-reaching refinements of the classical Calderón–Zygmund decomposition. These new Calderón–Zygmund decompositions in turn are produced with the help of new covering theorems that combine many remarkable features of classical results established by Besicovitch, Whitney and Wiener. In many cases the minimizers constructed in the book are stable (i.e., remain near-minimizers) under the action of Calderón–Zygmund singular integral operators.
The book is divided into two parts. While the new method is presented in great detail in the second part, the first is mainly devoted to the prerequisites needed for a self-contained presentation of the main topic. There we discuss the classical covering results mentioned above, various spectacular applications of the classical Calderón–Zygmund decompositions, and the relationship of all this to real interpolation. It also serves as a quick introduction to such important topics as spaces of smooth functions or singular integrals.
Reviews
From the reviews:
“The monograph is a good source of information on spaces of smooth functions and real interpolation methods. … the monograph could be a good reference on methods and results in the area. The book is highly recommended for specialists in approximation theory, harmonic analysis, functional analysis, and related areas. … the monograph should be interesting for specialists in applied mathematics and computer science. Graduate students specializing in analysis should find many interesting topics here, as well as motivation for further research.” (Alexander V. Tovstolis, Mathematical Reviews, August, 2013)
“This book consists of two parts. … Each chapter closes with comments, historical remarks and further references. Everybody who is interested in this topic should consult this important book. Without doubt, this monograph will stimulate further research.” (Manfred Tasche, zbMATH, Vol. 1270, 2013)Authors and Affiliations
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St. Petersburg Branch, Department of Mathematics, Steklov Mathematical Institute, St. Petersburg, Russia
Sergey Kislyakov
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, Department of Mathematics, Linköping University, Linköping, Sweden
Natan Kruglyak
Bibliographic Information
Book Title: Extremal Problems in Interpolation Theory, Whitney-Besicovitch Coverings, and Singular Integrals
Authors: Sergey Kislyakov, Natan Kruglyak
Series Title: Monografie Matematyczne
DOI: https://doi.org/10.1007/978-3-0348-0469-1
Publisher: Birkhäuser Basel
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Basel 2013
Hardcover ISBN: 978-3-0348-0468-4Published: 30 October 2012
Softcover ISBN: 978-3-0348-0752-4Published: 09 November 2014
eBook ISBN: 978-3-0348-0469-1Published: 29 October 2012
Series ISSN: 0077-0507
Series E-ISSN: 2297-0274
Edition Number: 1
Number of Pages: X, 322
Topics: Real Functions, Approximations and Expansions, Functional Analysis