LEADER 04086oam 2200541 450 001 9910790428703321 005 20190911112729.0 010 $a981-4458-77-5 035 $a(OCoLC)860388264 035 $a(MiFhGG)GVRL8RDO 035 $a(EXLCZ)992550000001114719 100 $a20140402h20132013 uy 0 101 0 $aeng 135 $aurun|---uuuua 181 $ctxt 182 $cc 183 $acr 200 10$aBochner-Riesz means on Euclidean spaces /$fShanzhen Lu, Beijing Normal University, China, Dunyan Yan, University of Chinese Academy of Sciences, China 210 1$aNew Jersey :$cWorld Scientific,$d[2013] 210 4$d?2013 215 $a1 online resource (viii, 376 pages) $cillustrations 225 0 $aGale eBooks 300 $aDescription based upon print version of record. 311 $a981-4458-76-7 311 $a1-299-83340-3 320 $aIncludes bibliographical references and index. 327 $aContents; Preface; 1 An introduction to multiple Fourier series; 1.1 Basic properties of multiple Fourier series; 1.2 Poisson summation formula; 1.3 Convergence and the opposite results; 1.4 Linear summation; 2 Bochner-Riesz means of multiple Fourier integral; 2.1 Localization principle and classic results on fixed-point convergence; 2.2 Lp-convergence; 2.3 Some basic facts on multipliers; 2.4 The disc conjecture and Fefferman theorem; 2.5 The Lp-boundedness of Bochner-Riesz operator T? with ? > 0; 2.6 Oscillatory integral and proof of Carleson-Sjolin theorem; 2.6.1 Oscillatory integrals 327 $a2.6.2 Proof of Carleson-Sjolin theorem2.7 Kakeya maximal function; 2.8 The restriction theorem of the Fourier transform; 2.9 The case of radial functions; 2.10 Almost everywhere convergence; 2.11 Commutator of Bochner-Riesz operator; 3 Bochner-Riesz means of multiple Fourier series; 3.1 The case of being over the critical index; 3.1.1 Bochner formula; 3.1.2 The localization theorem; 3.1.3 The maximal operator S?*; 3.2 The case of the critical index (general discussion); 3.2.1 Localization problems; 3.2.2 An example of being divergent almost everywhere 327 $a3.9 The saturation problem of the uniform approximation3.10 Strong summation; 4 The conjugate Fourier integral and series; 4.1 The conjugate integral and the estimate of the kernel; 4.2 Convergence of Bochner-Riesz means for conjugate Fourier integral; 4.3 The conjugate Fourier series; 4.4 Kernel of Bochner-Riesz means of conjugate Fourier series; 4.5 The maximal operator of the conjugate partial sum; 4.6 The relations between the conjugate series and integral; 4.7 Convergence of Bochner-Riesz means of conjugate Fourier series; 4.8 (C,1) means in the conjugate case 327 $a4.9 The strong summation of the conjugate Fourier series4.10 Approximation of continuous functions; Bibliography; Index 330 $aThis book mainly deals with the Bochner-Riesz means of multiple Fourier integral and series on Euclidean spaces. It aims to give a systematical introduction to the fundamental theories of the Bochner-Riesz means and important achievements attained in the last 50 years. For the Bochner-Riesz means of multiple Fourier integral, it includes the Fefferman theorem which negates the Disc multiplier conjecture, the famous Carleson-Sjo?lin theorem, and Carbery-Rubio de Francia-Vega's work on almost everywhere convergence of the Bochner-Riesz means below the critical index. For the Bochner-Riesz means o 606 $aFourier series 606 $aEuclidean algorithm 606 $aFourier series$xMathematical models 606 $aEuclidean algorithm$xMathematical models 615 0$aFourier series. 615 0$aEuclidean algorithm. 615 0$aFourier series$xMathematical models. 615 0$aEuclidean algorithm$xMathematical models. 676 $a515.2433 700 $aLu$b Shanzhen$f1939-$0629792 702 $aYan$b Dunyan 801 0$bMiFhGG 801 1$bMiFhGG 906 $aBOOK 912 $a9910790428703321 996 $aBochner-Riesz means on Euclidean spaces$93871844 997 $aUNINA