000 03994nam a22004935i 4500
001 978-1-4939-1194-3
003 DE-He213
005 20160302172504.0
007 cr nn 008mamaa
008 141117s2014 xxu| s |||| 0|eng d
020 _a9781493911943
_9978-1-4939-1194-3
024 7 _a10.1007/978-1-4939-1194-3
_2doi
050 4 _aQA403.5-404.5
072 7 _aPBKF
_2bicssc
072 7 _aMAT034000
_2bisacsh
082 0 4 _a515.2433
_223
100 1 _aGrafakos, Loukas.
_eauthor.
245 1 0 _aClassical Fourier Analysis
_h[electronic resource] /
_cby Loukas Grafakos.
250 _a3rd ed. 2014.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c2014.
300 _aXVII, 638 p. 14 illus., 2 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aGraduate Texts in Mathematics,
_x0072-5285 ;
_v249
505 0 _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.
520 _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.
650 0 _aMathematics.
650 0 _aHarmonic analysis.
650 0 _aFourier analysis.
650 0 _aFunctional analysis.
650 1 4 _aMathematics.
650 2 4 _aFourier Analysis.
650 2 4 _aAbstract Harmonic Analysis.
650 2 4 _aFunctional Analysis.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781493911936
830 0 _aGraduate Texts in Mathematics,
_x0072-5285 ;
_v249
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4939-1194-3
912 _aZDB-2-SMA
999 _c205919
_d205919