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On the (𝐶, α)-Means of Quadratic Partial Sums of Double Walsh–Kaczmarz–Fourier Series

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Published/Copyright: March 10, 2010
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Georgian Mathematical Journal
From the journal Volume 16 Issue 3

Abstract

The main aim of this paper is to prove that the (𝐶, α)-means of quadratic partial sums of double Walsh–Kaczmarz–Fourier series are of weak type (1, 1) and of type (𝑝, 𝑝) for all 1 < 𝑝 ≤ ∞ (0 < α < 1). Moreover, these (𝐶, α)-means converge to 𝑓 almost everywhere for any integrable function 𝑓.

Received: 2007-11-06
Published Online: 2010-03-10
Published in Print: 2009-September

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