000			03907nam a22004575i 4500
001			978-0-387-09432-8
003			DE-He213
005			20260127105208.0
007			cr nn 008mamaa
008			100301s2009 xxu| s |||| 0|eng d
020			_a9780387094328
020			_a99780387094328
024	7		_a10.1007/978-0-387-09432-8 _2doi
040			_cCICY
100	1		_aGrafakos, Loukas. _eauthor.
245	1	0	_aClassical Fourier Analysis _h[recurso electrónico] / _cby Loukas Grafakos.
264		1	_aNew York, NY : _bSpringer New York, _c2009.
300			_aXVI, 492 p. 10 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_arecurso en línea _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aGraduate Texts in Mathematics, _x0072-5285 ; _v249
505	0		_aPreface -- Lp Spaces and Interpolation -- Maximal Functions, Fourier Transform, and Distributions -- Fourier Analysis on the Torus -- Singular Integrals of Convolution Type -- Littlewood-Paley Theory and Multipliers -- Gamma and Beta Functions -- Bessel Functions -- Rademacher Functions -- Spherical Coordinates -- Some Trigonometric Identities and Inequalities -- Summation by Parts -- Basic Functional Analysis -- The Minimax Lemma -- The Schur Lemma -- The Whitney Decomposition of Open Sets in Rn -- Smoothness and Vanishing Moments -- Glossary -- References -- Index.
520			_aThe primary goal of these two volumes is to present the theoretical foundation of the field of Euclidean Harmonic analysis. The original edition was published as a single volume, but due to its size, scope, and the addition of new material, the second edition consists of two volumes. The present edition contains a new chapter on time-frequency analysis and the Carleson-Hunt theorem. The first volume contains the classical topics such as Interpolation, Fourier Series, the Fourier Transform, Maximal Functions, Singular Integrals, and Littlewood-Paley Theory. The second volume contains more recent topics such as Function Spaces, Atomic Decompositions, Singular Integrals of Nonconvolution Type, and Weighted Inequalities. These volumes are mainly addressed to graduate students in mathematics and are designed for a two-course sequence on the subject with additional material included for reference. The prerequisites for the first volume are satisfactory completion of courses in real and complex variables. The second volume assumes material from the first. This book is intended to present the selected topics in depth and stimulate further study. Although the emphasis falls on real variable methods in Euclidean spaces, a chapter is devoted to the fundamentals of analysis on the torus. This material is included for historical reasons, as the genesis of Fourier analysis can be found in trigonometric expansions of periodic functions in several variables. About the first edition: "Grafakos's book is very user-friendly with numerous examples illustrating the definitions and ideas... The treatment is thoroughly modern with free use of operators and functional analysis. Morever, unlike many authors, Grafakos has clearly spent a great deal of time preparing the exercises." - Kenneth Ross, MAA Online
650		0	_aMATHEMATICS.
650		0	_aHARMONIC ANALYSIS.
650		0	_aFOURIER ANALYSIS.
650		0	_aFUNCTIONAL ANALYSIS.
650	1	4	_aMATHEMATICS.
650	2	4	_aFUNCTIONAL ANALYSIS.
650	2	4	_aABSTRACT HARMONIC ANALYSIS.
650	2	4	_aFOURIER ANALYSIS.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780387094311
830		0	_aGraduate Texts in Mathematics, _x0072-5285 ; _v249
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-387-09432-8 _zVer el texto completo en las instalaciones del CICY
942			_2ddc _cER
999			_c55916 _d55916