Trigonometric Fourier Series and Their Conjugates /
This book presents in a coherent way the results obtained in the following aspects of the theory of multiple trigonometric Fourier series: the existence and properties of the conjugates and Hilbert transforms of integrable functions of several variables; convergence of Fourier series and their conju...
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht :
Springer Netherlands,
1996
|
| Series: | Mathematics and Its Applications ; ;
372 |
| Subjects: |
Table of Contents:
- Preface
- 1 Simple Trigonometric Series
- I. The Conjugation Operator and the Hilbert Transform
- II. Pointwise Convergence and Summability of Trigonometric Series
- III. Convergence and Summability of Trigonometric Fourier Series and Their Conjugates in the Spaces $$L^p \left(T \right), p \in \left] {0, + \infty } \right[$$
- IV. Some Approximating Properties of Cesaro Means of the Series $$ \sigma \left[f \right] $$ and $$ \bar \sigma \left[f \right] $$
- 2 Multiple Trigonometric Series
- I. Conjugate Functions and Hilbert Transforms of Functions of Several Variables
- II. Convergence and Summability at a Point or Almost Everywhere of Multiple Trigonometric Fourier Series and Their Conjugates
- III. Some Approximating Properties of n-Fold Cesaro Means of the Series $$ \sigma _n \left[f \right] $$ and $$ \sigma _n \left[{f, B} \right] $$
- IV. Convergence and Summability of Multiple Trigonometric Fourier Series and Their Conjugates in the Spaces $$ L^p \left({T^n } \right), p \in \left] {0, + \infty } \right] $$
- V. Summability of Series $$ \sigma _2 \left[f \right] $$ and $$ \bar \sigma _2 \left[{f, B} \right] $$ by a Method of the Marcinkiewicz Type