Extremal Problems in Interpolation Theory, Whitney-Besicovitch Coverings, and Singular Integrals

Released on by Sergey Kislyakov
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  • Extremal Problems in Interpolation Theory, Whitney-Besicovitch Coverings, and Singular Integrals Book Detail

  • Author : Sergey Kislyakov
  • Release Date : 2012-10-29
  • Publisher : Springer Science & Business Media
  • Genre : Mathematics
  • Pages : 320
  • ISBN 13 : 3034804695
  • File Size : 67,67 MB
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Extremal Problems in Interpolation Theory, Whitney-Besicovitch Coverings, and Singular Integrals by Sergey Kislyakov PDF Summary

Book Description: 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.

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Classical Fourier Analysis

Classical Fourier Analysis

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The main goal of this text is to present the theoretical foundation of the field of Fourier analysis on Euclidean spaces. It covers classical topics such as int