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020 _a9783034804691
_9978-3-0348-0469-1
024 7 _a10.1007/978-3-0348-0469-1
_2doi
050 4 _aQA331.5
072 7 _aPBKB
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aMAT037000
_2bisacsh
082 0 4 _a515.8
_223
100 1 _aKislyakov, Sergey.
_eauthor.
245 1 0 _aExtremal Problems in Interpolation Theory, Whitney-Besicovitch Coverings, and Singular Integrals
_h[electronic resource] /
_cby Sergey Kislyakov, Natan Kruglyak.
264 1 _aBasel :
_bSpringer Basel :
_bImprint: Birkhäuser,
_c2013.
300 _aX, 322 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aMonografie Matematyczne ;
_v74
505 0 _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.
520 _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.
650 0 _aMathematics.
650 0 _aApproximation theory.
650 0 _aFunctional analysis.
650 0 _aFunctions of real variables.
650 1 4 _aMathematics.
650 2 4 _aReal Functions.
650 2 4 _aApproximations and Expansions.
650 2 4 _aFunctional Analysis.
700 1 _aKruglyak, Natan.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783034804684
830 0 _aMonografie Matematyczne ;
_v74
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-0348-0469-1
912 _aZDB-2-SMA
942 _2Dewey Decimal Classification
_ceBooks
999 _c45217
_d45217