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Pointwise Convergence of Fourier Series
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Catalogue Information
Field name
Details
Dewey Class
515.2433
Title
Pointwise Convergence of Fourier Series ([EBook] /) / by Juan Arias de Reyna.
Author
Arias de Reyna, Juan
Other name(s)
SpringerLink (Online service)
Publication
Berlin, Heidelberg : : Springer Berlin Heidelberg : : Imprint: Springer, , 2002.
Physical Details
XVIII, 179 p. : online resource.
Series
Lecture Notes in Mathematics
0075-8434 ; ; 1785
ISBN
9783540458227
Summary Note
This 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.:
Contents note
Part 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.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site
http://dx.doi.org/10.1007/b83346
Links to Related Works
Subject References:
Fourier Analysis
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Mathematics
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Authors:
Arias de Reyna, Juan
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Corporate Authors:
SpringerLink (Online service)
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Series:
Lecture Notes in Mathematics
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Classification:
515.2433
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