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Extremal Problems in Interpolation Theory, Whitney-Besicovitch Coverings, and Singular Integrals
Steklov Mathematical Institute, St. Petersburg Branch, St. Petersburg, Russia.
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
2013 (English)Book (Other academic)
Abstract [en]

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.

Place, publisher, year, edition, pages
Basel: Springer, 2013. , 316 p.
, Monografie Matematyczne, ISSN 0077-0507 ; 74
Keyword [en]
Mathematics, Functional analysis, Real Functions, Approximations and Expansions, Functional Analysis
National Category
URN: urn:nbn:se:liu:diva-86188ISBN: 978-3-0348-0468-4ISBN: 978-3-0348-0469-1OAI: diva2:575705
Available from: 2012-12-11 Created: 2012-12-10 Last updated: 2014-11-27Bibliographically approved

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Kruglyak, Natan
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Mathematics and Applied MathematicsThe Institute of Technology

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