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Extremal Problems in Interpolation Theory, Whitney-Besicovitch Coverings, and Singular Integrals (Paperback, 2013 ed.)
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Extremal Problems in Interpolation Theory, Whitney-Besicovitch Coverings, and Singular Integrals (Paperback, 2013 ed.)
Series: Monografie Matematyczne, 74
Expected to ship within 10 - 15 working days
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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 Calderon-Zygmund
decomposition. These new Calderon-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 Calderon-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 Calderon-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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