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Summability of Multi-Dimensional Trigonometric Fourier Series
Hardy spaces Hp-atom interpolation Fourier series circular triangu-lar cubic and rectangular summability
2012/6/30
We consider the summability of one- and multi-dimensional trigonometric Fourier series. The Fej{\'e}r and Riesz summability methods are investigated in detail. Different types of summation and converg...
Pointwise convergence of vector-valued Fourier series
Pointwise convergence vector-valued Fourier series Functional Analysis
2012/5/24
We prove a vector-valued version of Carleson's theorem: Let Y=[X,H]_t be a complex interpolation space between a UMD space X and a Hilbert space H. For p\in(1,\infty) and f\in L^p(T;Y), the partial su...
Approximation of functions from Lp(w)b by matrix means of their Fourier series
Rate of approximation summability of Fourier series Lipschitz classes
2012/4/16
We formulate some special conditions for the integrable functions and moduli of continuity. We give the results on rate of approximation of such functions by matrix means of their Fourier series, wher...
Local Property of Absolute Weighted Mean Summability of Fourier Series
Local property Fourier series absolute summability H¨older’s inequality Minkowski’s inequality
2009/6/16
We obtain a general theorem on a local property of j T jk summability of factored
Fourier series generalizing some previous result due to Rhoades and Savas [5]. Another
result concerning j T jk of F...
Negative Results Concerning Fourier Series on the Complete Product of $\mathcal{S}_3$
Fourier series Walsh-system Vilenkin systems Representative product systems
2010/1/22
The aim of this paper is to continue the studies about convergence in -norm of the Fourier series based on representative product systems on the complete product of finite groups. We restrict our atte...
Cesáro Means of $N$-multiple Trigonometric Fourier Series
Trigonometric system Cesáro means Summability
2008/7/1
Cesáro Means of $N$-multiple Trigonometric Fourier Series.
Localization of Factored Fourier Series.
Maximal Operators of Fejér Means of Vilenkin-Fourier Series
Fejér Means Maximal Operators Vilenkin-Fourier Series
2008/6/30
Maximal Operators of Fejér Means of Vilenkin-Fourier Series.
On the Absolute Convergence of Small Gaps Fourier Series of Functions of $\varphi \bigwedge BV $
Functions Small Gaps Fourie Absolute Convergence
2008/6/27
On the Absolute Convergence of Small Gaps Fourier Series of Functions of $\varphi \bigwedge BV $.
On the Absolute Convergence of Small Gaps Fourier Series of Functions of $\bigwedge BV^{(p)}$
Fourier series with small gaps Absolute convergence of Fourier series p-$bigwedge $-bounded variation
2008/6/27
On the Absolute Convergence of Small Gaps Fourier Series of Functions of $\bigwedge BV^{(p)}$.
Power-Monotone Sequences and Fourier Series with Positive Coefficients
Fourier series Fourier coefficients modulus of continuity quasi power-monotone sequences
2008/6/27
M. and S. Izumi [2] and the present author [7] have extended certain theorems of R.P. Boas [1] concerning the Fourier coefficients of functions belonging to the Lipschitz classes. Very recently L. Lei...
Power-monotone sequences and Fourier series with positive coefficients
Fourier series Fourier coefficients Lipschitz classes modulus of continuity cosine and sine series quasi power-monotone sequences
2008/6/27
J. Németh has extended several basic theorems of R.P. Boas Jr. pertaining to Fourier series with positive coefficients from Lipschitz classes to generalized Lipschitz classes. The goal of the present ...
Some Results on $L^1$ Approximation of the $r$-th Derivate of Fourier Series
$L^1$-approximation Fourier series Sidon-Telyakovskii class Telyakovskii inequality
2008/6/26
Some Results on $L^1$ Approximation of the $r$-th Derivate of Fourier Series.
<正> 1.Introduction.It is classical that,if the Fourier series of a function ψ(t) ofbounded variation is (?) sin nt,the sequence (?) is bounded.This resultcannot be improved.“For,the function (?) whose...
Approximation of Continuous Funtions Using Fejer Sums of Jacobi-Fourier Series
Jacobi-Fourier series Fejer sums continuous funtions approximation
2012/10/11
The pointwise estimates of approximation of continuous function() f xby Fejer sums ,(,)nf xαβσ of its Jacobi-Fourier series have been investigated, which improved the results of Li Z K for points.1 x ...