Pointwise convergence of Fourier series /
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...
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| Format: | Book |
| Language: | English |
| Published: |
Berlin : London :
Springer,
c2002
Berlin ; New York : Springer Berlin Heidelberg : Imprint: Springer, c2002 Berlin ; New York : ©2002 Berlin, Heidelberg : 2002 |
| Series: | Lecture Notes in Mathematics,
1785 Lecture notes in mathematics (Springer-Verlag) ; 1785 Lecture notes in mathematics (Springer-Verlag) 1785 |
| Subjects: |
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| 100 | 1 | |a Arias de Reyna, Juan, |d 1947- |1 http://viaf.org/viaf/44522839 | |
| 100 | 1 | |a Arias de Reyna, Juan, |d 1947- |e author |4 http://id.loc.gov/vocabulary/relators/aut | |
| 100 | 1 | |a Arias de Reyna, Juan, |d 1947- | |
| 245 | 1 | 0 | |a Pointwise convergence of Fourier series / |c Juan Arias de Reyna |
| 260 | |a Berlin : |a London : |b Springer, |c c2002 | ||
| 260 | |a Berlin ; |a New York : |b Springer, |c c2002 | ||
| 260 | |a Berlin ; |a New York : |b Springer, |c ©2002 | ||
| 264 | 1 | |a Berlin, Heidelberg : |b Springer Berlin Heidelberg : |b Imprint: Springer, |c 2002 | |
| 300 | |a 1 online resource (XVIII, 179 pages) | ||
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| 300 | |a xviii, 175 p. : |b ill. ; |c 24 cm | ||
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| 490 | 1 | |a Lecture Notes in Mathematics, |x 0075-8434 ; |v 1785 | |
| 490 | 1 | |a Lecture notes in mathematics |x 0075-8434 ; |v 1785 | |
| 490 | 1 | |a Lecture notes in mathematics, |x 0075-8434 ; |v 1785 | |
| 504 | |a Includes bibliographical references (p. [167]-169) and index | ||
| 504 | |a Includes bibliographical references (pages 167-169) and index | ||
| 504 | |a Includes bibliographical references and index | ||
| 505 | 0 | |a 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 | |
| 505 | 0 | 0 | |g Pt. I |t Fourier series and Hilbert Transform -- |g 1. |t Hardy-Littlewood maximal function -- |g 2. |t Fourier Series -- |g 3. |t Hilbert Transform -- |g Pt. II. |t The Carleson-Hunt Theorem -- |g 4. |t The Basic Step -- |g 5. |t Maximal inequalities -- |g 6. |t Growth of Partial Sums -- |g 7. |t Carleson Analysis of the Function -- |g 8. |t Allowed pairs -- |g 9. |t Pair Interchange Theorems -- |g 10. |t All together -- |g Pt. III. |t Consequences -- |g 11. |t Some spaces of functions -- |g 12. |t The Maximal Operator of Fourier series. |
| 506 | |a Restricted for use by site license | ||
| 520 | |a 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, Sjlin, 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 $cal L^1$, filling a well-known gap in the literature | ||
| 520 | |a 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 | ||
| 530 | |a Also available online via the World Wide Web; access restricted to licensed sites/users | ||
| 530 | |a Full text also available on the Internet to registered users | ||
| 596 | |a 4 | ||
| 650 | 0 | |a Convergence | |
| 650 | 0 | |a Fourier analysis | |
| 650 | 0 | |a Fourier series | |
| 650 | 7 | |a Convergence |2 fast | |
| 650 | 7 | |a Fourier analysis |2 fast | |
| 650 | 7 | |a Fourier series |2 fast | |
| 650 | 1 | 4 | |a Fourier Analysis |
| 655 | 4 | |a Electronic books | |
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| 776 | 0 | 8 | |i Printed edition: |z 9783540432708 |
| 776 | 0 | 8 | |i Printed edition: |z 9783662184127 |
| 776 | 1 | |w (OCoLC)50039399 | |
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