LEADER 04753nam 22006975 450 001 9910299988703321 005 20251116135949.0 010 $a1-4939-1194-5 024 7 $a10.1007/978-1-4939-1194-3 035 $a(CKB)3710000000306051 035 $a(SSID)ssj0001386400 035 $a(PQKBManifestationID)11752488 035 $a(PQKBTitleCode)TC0001386400 035 $a(PQKBWorkID)11350218 035 $a(PQKB)11704010 035 $a(DE-He213)978-1-4939-1194-3 035 $a(MiAaPQ)EBC6311589 035 $a(MiAaPQ)EBC5595740 035 $a(Au-PeEL)EBL5595740 035 $a(OCoLC)897130755 035 $a(PPN)183096053 035 $a(EXLCZ)993710000000306051 100 $a20141117d2014 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aClassical Fourier Analysis /$fby Loukas Grafakos 205 $a3rd ed. 2014. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d2014. 215 $a1 online resource (XVII, 638 p. 14 illus., 2 illus. in color.) 225 1 $aGraduate Texts in Mathematics,$x0072-5285 ;$v249 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a1-4939-1193-7 320 $aIncludes bibliographical references and index. 327 $aPreface -- 1. Lp Spaces and Interpolation -- 2. Maximal Functions, Fourier Transform, and Distributions -- 3. Fourier Series -- 4. Topics on Fourier Series -- 5. Singular Integrals of Convolution Type -- 6. Littlewood?Paley Theory and Multipliers -- 7. Weighted Inequalities -- A. Gamma and Beta Functions -- B. Bessel Functions -- C. Rademacher Functions -- D. Spherical Coordinates -- E. Some Trigonometric Identities and Inequalities -- F. Summation by Parts -- G. Basic Functional Analysis -- H. The Minimax Lemma -- I. Taylor's and Mean Value Theorem in Several Variables -- J. The Whitney Decomposition of Open Sets in Rn -- Glossary -- References -- Index. 330 $aThe main goal of this text is to present the theoretical foundation of the field of Fourier analysis on Euclidean spaces. It covers classical topics such as interpolation, Fourier series, the Fourier transform, maximal functions, singular integrals, and Littlewood?Paley theory. The primary readership is intended to be graduate students in mathematics with the prerequisite including satisfactory completion of courses in real and complex variables. The coverage of topics and exposition style are designed to leave no gaps in understanding and stimulate further study. This third edition includes new Sections 3.5, 4.4, 4.5 as well as a new chapter on ?Weighted Inequalities,? which has been moved from GTM 250, 2nd Edition. Appendices I and B.9 are also new to this edition. Countless corrections and improvements have been made to the material from the second edition. Additions and improvements include: more examples and applications, new and more relevant hints for the existing exercises, new exercises, and improved references. Reviews from the Second Edition: ?The books cover a large amount of mathematics. They are certainly a valuable and useful addition to the existing literature and can serve as textbooks or as reference books. Students will especially appreciate the extensive collection of exercises.? ?Andreas Seager, Mathematical Reviews ?This book is very interesting and useful. It is not only a good textbook, but also an indispensable and valuable reference for researchers who are working on analysis and partial differential equations. The readers will certainly benefit a lot from the detailed proofs and the numerous exercises.? ?Yang Dachun, zbMATH. 410 0$aGraduate Texts in Mathematics,$x0072-5285 ;$v249 606 $aFourier analysis 606 $aHarmonic analysis 606 $aFunctional analysis 606 $aFourier Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12058 606 $aAbstract Harmonic Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12015 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 615 0$aFourier analysis. 615 0$aHarmonic analysis. 615 0$aFunctional analysis. 615 14$aFourier Analysis. 615 24$aAbstract Harmonic Analysis. 615 24$aFunctional Analysis. 676 $a515.2433 700 $aGrafakos$b Loukas$4aut$4http://id.loc.gov/vocabulary/relators/aut$0298204 701 $aGrafakos$b Loukas$0298204 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299988703321 996 $aClassical Fourier analysis$9229858 997 $aUNINA