Pointwise Convergence of Fourier Series

• Main Author: Arias de Reyna, Juan (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2002.
• Edition: 1st ed. 2002.
• Series: Lecture Notes in Mathematics, 1785
• Subjects: Fourier analysis.; Fourier Analysis.

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 t...

Table of Contents:

• 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.