Author | Zhizhiashvili, Levan. author |
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Title | Trigonometric Fourier Series and Their Conjugates [electronic resource] / by Levan Zhizhiashvili |
Imprint | Dordrecht : Springer Netherlands, 1996 |
Connect to | http://dx.doi.org/10.1007/978-94-009-0283-1 |
Descript | XII, 308 p. online resource |
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 $$L̂p \left( T \right),p \in \left] {0, + \infty } \right[$$ -- 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 $$ L̂p \left( {T̂n } \right),p \in \left] {0, + \infty } \right] $$ -- V. Summability of Series $$ \sigma _2 \left[ f \right] $$ and $$ \bar \sigma _2 \left[ {f,B} \right] $$ by a Method of the Marcinkiewicz Type