A convergence test for Walsh-Fourier series
نویسندگان
چکیده
منابع مشابه
Statistical Convergence of Walsh-fourier Series
This is a brief and concise account of the basic concepts and results on statistical convergence, strong Cesàro summability and Walsh-Fourier series. To emphasize the significance of statistical convergence, for example we mention the fact that the one-dimensional Walsh-Fourier series of an integrable (in Lebesgue’s sense) function may be divergent almost everywhere, but it is statistically con...
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In this paper we present some results on convergence and summability of oneand multi-dimensional trigonometric andWalsh-Fourier series. The Fejér and Cesàro summability methods are investigated. We will prove that the maximal operator of the summability means is bounded from the corresponding classical or martingale Hardy space Hp to Lp for some p > p0. For p = 1 we obtain a weak type inequalit...
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Every function f(x) which is of period 1 and Lebesgue integrable on [0, 1 ] may be expanded in a Walsh-Fourier series(3), f(x)~ ?.?=n ak\pk(x), where ak=fof(x)ypk(x)dx, k=0, 1, 2, • • • . Fine exhibited some of the basic similarities and differences between the trigonometric orthonormal system and the Walsh system. He identified the Walsh functions with the full set of characters of the dyadic ...
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We show that a general Walsh series is the Walsh-Fourier series of a function f ∈ Lp[0, 1] for 1 ≤ p <∞ if and only if its sequence of partial sums contains a relatively weakly compact subsequence. Several other criteria are established for the case where f ∈ LΦ[0, 1], the Orlicz space generated by an N -function Φ. Mathematics subject classification (2000): 42C10, 46E30
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The main aim of this paper is to prove that the maximal operator of a subsequence of the (one-dimensional) logarithmic means of Walsh-Kaczmarz-Fourier series is of weak type (1,1) . Moreover, we prove that the maximal operator of the logarithmic means of quadratical partial sums of double Walsh-Kaczmarz-Fourier series is of weak type (1,1) , provided that the supremum in the maximal operator is...
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ژورنال
عنوان ژورنال: Tohoku Mathematical Journal
سال: 1954
ISSN: 0040-8735
DOI: 10.2748/tmj/1178245184