| UNIFORM CONVERGENCE OF CESARO MEANS OF NEGATIVE ORDER OF DOUBLE TRIGONOMETRIC FOURIER SERIES |
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| 作者姓名： | U. Goginava |
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| 作者单位： | Institute of Mathematics Faculty of Exact and Natural Sciences Tbilisi State University Chavchavadze Str. 1, Tbilisi 0128 Georgia |
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| 摘 要： | In this paper we prove that iff ∈ C(-π,π]2) and the function f is bounded partial p-variation for some p ∈ 1, ∞), then the double trigonometric Fourier series of a function f is uniformly (C;-α,-β) summable (α β＜ 1/p,α,β＞ 0) in the sense of Pringsheim. If α β≥ 1/p, then there exists a continuous function f0 of bounded partial double trigonometric Fourier series of fo diverge over cubes.
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| 关 键 词： | 傅立叶级数 有限变分 Cesà ro均值 收敛性 |
| 收稿时间： | 16 January 2007 |
| 修稿时间： | 2007-01-16 |
Uniform convergence of Cesàro means of negative order of double trigonometric Fourier series |
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| U. Goginava.UNIFORM CONVERGENCE OF CESARO MEANS OF NEGATIVE ORDER OF DOUBLE TRIGONOMETRIC FOURIER SERIES[J].Analysis in Theory and Applications,2007,23(3):255-265. |
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| Authors: | U Goginava |
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| Institution: | (1) Institute of Mathematics Faculty of Exact and Natural Sciences, Tbilisi State University, Chavchavadze Str. 1, Tbilisi, 0128, Georgia |
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| Abstract: | In this paper we prove that if f ∊ C(−π, π]2) and the function f is bounded partial p-variation for some p ∊ 1,+ ∞), then the double trigonometric Fourier series of a function f is uniformly (C;−α,−β) summable (α+β> 1/p, α, β> 0) in the sense of Pringsheim. If α + β ≥ 1/p, then there exists a continuous function f
0 of bounded partial p-variation on −π, π]2 such that the Cesàro (C;−α,−β) means σ
n,m
−α,−β
(f
0;0,0) of the double trigonometric Fourier series of f
0 diverge over cubes.
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| Keywords: | Fourier series bounded variation Cesàro means CONVERGENCE FOURIER SERIES DOUBLE ORDER NEGATIVE continuous function diverge cubes sense double Fourier series bounded partial paper prove |
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