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Cesàro Means of Trigonometric Fourier Series
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U. Goginava
Published/Copyright:
February 26, 2010
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(𝑛α𝑤(1/𝑛)) where 𝑤(·) is a modulus of continuity. In this paper we show that this estimation is non-amplifiable for 𝑝 = 1.
Key words and phrases:: Trigonometric Fourier series; Cesàro means
Received: 2001-01-18
Published Online: 2010-02-26
Published in Print: 2002-March
© Heldermann Verlag
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Articles in the same Issue
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- Existence and Properties of ℎ-Sets
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- Estimates of a Stabilization Rate as 𝑡 → ∞ Solutions of a Nonlinear Integro-Differential Equation
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- The Bochner Mean Square Deviation and Law of Large Numbers for Squares of Random Elements in Banach Lattices
- A Strong Solution of an Evolution Problem with Integral Conditions
- On Some Properties of 𝑟-Maximal Sets and 𝑄1–𝑁-Reducibility
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