OnL1-convergence of 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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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 1978
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s016117127800006x