Extremal problems in interpolation theory, Whitney-Besicovitch coverings, and singular integrals

In this book, a unified method is suggested for the construction of near-minimizers for certain important functional, which arise in approximation, harmonic analysis and ill-posed problems and are most widely used in interpolation theory. The constructions are based on far-reaching refinements of the classicalCalderón-Zygmund decomposition. In their turn, these new Calderón-Zygmund decompositions are produced with the help of new covering theorems that combine many remarkable features of classical results due to 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 consists of two parts. While the new method is exposed in great detail in the second part, the first one is mainly devoted to the prerequisites needed for a self-contained presentation of the main topic. The classical covering results are discussed as well as various spectacular applications of the classical Calderón-Zygmund decompositions, and their relationship with real interpolation. It also serves as a quick introduction to such important topics as spaces of smooth functions or singular integrals.

• ISBN: 978-3-0348-0468-4
• Editorial: Birkhaüser
• Encuadernacion: Cartoné
• Fecha Publicación: 28/09/2012
• Nº Volúmenes: 1
• Idioma: Inglés