000			02930nam a22004575i 4500
001			978-3-540-45822-7
003			DE-He213
005			20160624101821.0
007			cr nn 008mamaa
008			121227s2002 gw | s |||| 0|eng d
020			_a9783540458227 _9978-3-540-45822-7
024	7		_a10.1007/b83346 _2doi
050		4	_aQA403.5-404.5
072		7	_aPBKF _2bicssc
072		7	_aMAT034000 _2bisacsh
082	0	4	_a515.2433 _223
100	1		_aArias de Reyna, Juan. _eauthor.
245	1	0	_aPointwise Convergence of Fourier Series _h[electronic resource] / _cby Juan Arias de Reyna.
260		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2002.
264		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2002.
300			_aXVIII, 179 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aLecture Notes in Mathematics, _x1617-9692 ; _v1785
505	0		_aPart I. Fourier series and Hilbert Transform -- Hardy-Littlewood maximal function -- Fourier Series -- Hilbert Transform -- Part II. The Carleson-Hunt Theorem -- The Basic Step -- Maximal inequalities -- Growth of Partial Sums -- Carleson Analysis of the Function -- Allowed pairs -- Pair Interchange Theorems -- All together -- Part III. Consequences -- Some spaces of functions -- The Maximal Operator of Fourier series.
520			_aThis book contains a detailed exposition of Carleson-Hunt theorem following the proof of Carleson: to this day this is the only one giving better bounds. It points out the motivation of every step in the proof. Thus the Carleson-Hunt theorem becomes accessible to any analyst.The book also contains the first detailed exposition of the fine results of Hunt, Sjölin, Soria, etc on the convergence of Fourier Series. Its final chapters present original material. With both Fefferman's proof and the recent one of Lacey and Thiele in print, it becomes more important than ever to understand and compare these two related proofs with that of Carleson and Hunt. These alternative proofs do not yield all the results of the Carleson-Hunt proof. The intention of this monograph is to make Carleson's proof accessible to a wider audience, and to explain its consequences for the pointwise convergence of Fourier series for functions in spaces near $äcal Lü^1$, filling a well-known gap in the literature.
650		0	_aMathematics.
650		0	_aFourier analysis.
650	1	4	_aMathematics.
650	2	4	_aFourier Analysis.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783540432708
786			_dSpringer
830		0	_aLecture Notes in Mathematics, _x1617-9692 ; _v1785
856	4	0	_uhttp://dx.doi.org/10.1007/b83346
942			_2EBK1345 _cEBK
999			_c30639 _d30639