Cesàro Means of Trigonometric Fourier Series

2002 ◽  
Vol 9 (1) ◽  
pp. 53-56
Author(s):  
U. Goginava
Keyword(s):  
Fourier Series ◽  
Modulus Of Continuity ◽  
Trigonometric Fourier Series ◽  
Cesàro Means ◽  
Cesàro Mean ◽  
Cesaro Means ◽  
Cesáro Means ◽  
Cesaro Mean

Abstract L. Zhizhiashvili proved that if for some 𝑝, 1 ≤ 𝑝 ≤ ∞, and α ∈ (0, 1), then the 𝐿𝑝-deviation of 𝑓 from its Cesàro mean is 𝑂(𝑛 α 𝑤(1/𝑛)) where 𝑤(·) is a modulus of continuity. In this paper we show that this estimation is non-amplifiable for 𝑝 = 1.

On the Approximate Properties of Generalized Cesàro Means of Conjugate Trigonometric Fourier Series

2009 ◽  
Vol 16 (3) ◽  
pp. 413-425
Author(s):  
Teimuraz Akhobadze
Keyword(s):  
Fourier Series ◽  
Continuous Functions ◽  
Trigonometric Fourier Series ◽  
Cesàro Means ◽  
Space Of Continuous Functions ◽  
Cesaro Means ◽  
Cesáro Means ◽  
Generalized Cesàro Means

Abstract The behavior of generalized Cesàro (𝐶, α 𝑛)-means (α 𝑛 ∈ (–1, 0), 𝑛 = 1, 2, . . .) of conjugate trigonometric Fourier series of 𝐻𝑤 classes in the space of continuous functions is studied.

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