Equiconvergence of expansions in multiple trigonometric Fourier series and integrals in the case of a lacunary sequence of partial sums

2013 ◽  
Vol 87 (3) ◽  
pp. 296-299
Author(s):  
I. L. Bloshanskii ◽  
D. A. Grafov
Keyword(s):  
Fourier Series ◽  
Lacunary Sequence ◽  
Trigonometric Fourier Series ◽  
Partial Sums ◽  
Multiple Trigonometric Fourier Series

Trigonometric Fourier series and Walsh-Fourier series with lacunary sequence of partial sums

2013 ◽  
Vol 93 (1-2) ◽  
pp. 332-336
Author(s):  
S. K. Bloshanskaya ◽  
I. L. Bloshanskii ◽  
O. V. Lifantseva
Keyword(s):  
Fourier Series ◽  
Lacunary Sequence ◽  
Trigonometric Fourier Series ◽  
Partial Sums

scholarly journals The multipliers of multiple trigonometric Fourier series

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Aizhan Ydyrys ◽  
Lyazzat Sarybekova ◽  
Nazerke Tleukhanova
Keyword(s):  
Fourier Series ◽  
Sufficient Conditions ◽  
Regular System ◽  
Multiple Fourier Series ◽  
Trigonometric Fourier Series ◽  
Lorentz Spaces ◽  
Complex Numbers ◽  
Multiple Trigonometric Fourier Series

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.

On an Estimate of the Partial Sums of Vilenkin-Fourier

1991 ◽  
Vol 34 (3) ◽  
pp. 426-432
Author(s):  
Wo-Sang Young
Keyword(s):  
Fourier Series ◽  
Exponential Type ◽  
Maximal Function ◽  
Lacunary Sequence ◽  
Partial Sums ◽  
Littlewood Maximal Function

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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