LEADER 03925nam 2200613 a 450 001 9910438140903321 005 20200520144314.0 010 $a1-283-90994-4 010 $a3-0348-0469-5 024 7 $a10.1007/978-3-0348-0469-1 035 $a(CKB)2670000000279830 035 $a(EBL)1082164 035 $a(OCoLC)819631473 035 $a(SSID)ssj0000798613 035 $a(PQKBManifestationID)11518137 035 $a(PQKBTitleCode)TC0000798613 035 $a(PQKBWorkID)10754616 035 $a(PQKB)11045796 035 $a(DE-He213)978-3-0348-0469-1 035 $a(MiAaPQ)EBC1082164 035 $a(PPN)168307308 035 $a(EXLCZ)992670000000279830 100 $a20121004d2013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aExtremal problems in interpolation theory, Whitney-Besicovitch coverings, and singular integrals /$fSergey Kislyakov, Natan Kruglyak 205 $a1st ed. 2013. 210 $aNew York $cSpringer$d2013 215 $a1 online resource (319 p.) 225 0$aMonografie matematyczne ;$vv. 74 300 $aDescription based upon print version of record. 311 $a3-0348-0752-X 311 $a3-0348-0468-7 320 $aIncludes bibliographical references and index. 327 $aPreface -- Introduction -- Definitions, notation, and some standard facts -- Part 1. Background -- Chapter 1. Classical Calderón?Zygmund decomposition and real interpolation -- Chapter 2. Singular integrals -- Chapter 3. Classical covering theorems -- Chapter 4. Spaces of smooth functions and operators on them -- Chapter 5. Some topics in interpolation -- Chapter 6. Regularization for Banach spaces -- Chapter 7. Stability for analytic Hardy spaces -- Part 2. Advanced theory -- Chapter 8. Controlled coverings -- Chapter 9. Construction of near-minimizers -- Chapter 10. Stability of near-minimizers -- Chapter 11. The omitted case of a limit exponent -- Chapter A. Appendix. Near-minimizers for Brudnyi and Triebel?Lizorkin spaces -- Notes and remarks -- Bibliography -- Index. 330 $aIn this book we suggest a unified method of constructing near-minimizers for certain important functionals arising in approximation, harmonic analysis and ill-posed problems and most widely used in interpolation theory. The constructions are based on far-reaching refinements of the classical Calderón?Zygmund decomposition. These new Calderón?Zygmund decompositions in turn are produced with the help of new covering theorems that combine many remarkable features of classical results established by Besicovitch, Whitney and Wiener. In many cases the minimizers constructed in the book are stable (i.e., remain near-minimizers) under the action of Calderón?Zygmund singular integral operators. The book is divided into two parts. While the new method is presented in great detail in the second part, the first is mainly devoted to the prerequisites needed for a self-contained presentation of the main topic. There we discuss the classical covering results mentioned above, various spectacular applications of the classical Calderón?Zygmund decompositions, and the relationship of all this to real interpolation. It also serves as a quick introduction to such important topics as spaces of smooth functions or singular integrals. 410 0$aMonografie Matematyczne,$x0077-0507 ;$v74 606 $aInterpolation 606 $aInterpolation spaces 615 0$aInterpolation. 615 0$aInterpolation spaces. 676 $a515.2433 700 $aKislyakov$b Sergey$0732256 701 $aKruglyak$b Natan$01752384 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910438140903321 996 $aExtremal problems in interpolation theory, Whitney-Besicovitch coverings, and singular integrals$94187658 997 $aUNINA