scholarly journals Sufficient conditions for convergence of multiple Fourier series with J k -lacunary sequence of rectangular partial sums in terms of Weyl multipliers

2017 ◽  
Vol 83 (34) ◽  
pp. 511-537
Author(s):  
Igor L. Bloshanskii ◽  
S. K. Bloshanskaya ◽  
Denis A. Grafov
2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
A. A. Rakhimov

We study special partial sums of multiple Fourier series of distributions. We obtain sufficient conditions of summation of Riesz means of Fourier expansions of distributions with compact support.


1992 ◽  
Vol 15 (2) ◽  
pp. 209-220 ◽  
Author(s):  
Ferenc Móricz

We study the rate of approximation by rectangular partial sums, Cesàro means, and de la Vallée Poussin means of double Walsh-Fourier series of a function in a homogeneous Banach spaceX. In particular,Xmay beLp(I2), where1≦p<∞andI2=[0,1)×[0,1), orCW(I2), the latter being the collection of uniformlyW-continuous functions onI2. We extend the results by Watari, Fine, Yano, Jastrebova, Bljumin, Esfahanizadeh and Siddiqi from univariate to multivariate cases. As by-products, we deduce sufficient conditions for convergence inLp(I2)-norm and uniform convergence onI2as well as characterizations of Lipschitz classes of functions. At the end, we raise three problems.


2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Aizhan Ydyrys ◽  
Lyazzat Sarybekova ◽  
Nazerke Tleukhanova

Abstract We study the multipliers of multiple Fourier series for a regular system on anisotropic Lorentz spaces. In particular, the sufficient conditions for a sequence of complex numbers {λk}k∈Zn in order to make it a multiplier of multiple trigonometric Fourier series from Lp[0; 1]n to Lq[0; 1]n , p > q. These conditions include conditions Lizorkin theorem on multipliers.


2019 ◽  
Vol 489 (1) ◽  
pp. 7-10
Author(s):  
R. R. Ashurov

In this paper the generalized localization principle for the spherical partial sums of the multiple Fourier series in the L2-class is proved, that is, if f L2 (ТN) and f = 0 on an open set ТN then it is shown that the spherical partial sums of this function converge to zero almost - ​everywhere on . It has been previously known that the generalized localization is not valid in Lp (TN) when 1 p 2. Thus the problem of generalized localization for the spherical partial sums is completely solved in Lp (TN), p 1: if p 2 then we have the generalized localization and if p 2, then the generalized localization fails.


1991 ◽  
Vol 34 (3) ◽  
pp. 426-432
Author(s):  
Wo-Sang Young

AbstractWe show that the partial sums Snf of the Vilenkin-Fourier series of f ∊ L1 are of exponential type off any set where the Hardy-Littlewood maximal function of f is bounded. It then follows that Snkf(x) = o(log log nk) a.e. for any lacunary sequence {nk}. Our results are Vilenkin-Fourier series analogues of those of R. A. Hunt [1].


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