منابع مشابه
Almost Everywhere Strong Summability of Two-dimensional Walsh-fourier Series
A BMO-estimation of two-dimensional Walsh-Fourier series is proved from which an almost everywhere exponential summability of quadratic partial sums of double Walsh-Fourier series is derived.
متن کاملFurther result on the strong summability of Fourier series
This article deals with some special cases which are extension of the strong summability of Fourier series with constant factor. We obtain a new equivalent form of inequalities A 2π 0 φ(e iθ) r dθ ≤ 2π 0 1 0 (1 − ρ) φ (z) 2 dρ r/2 dθ ≤ B 2π 0 φ(e iθ) r dθ, (1) 2π 0 1 0 (1 − ρ) q−1 φ (z) q dρ r/q dθ ≤ C 2π 0 φ(e iθ) r dθ, (2) D 2π 0 φ(e iθ) r dθ ≤ 2π 0 1 0 (1 − ρ) p−1 φ (z) p dρ r/p dθ.
متن کاملOn Walsh-fourier Series^)
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 ...
متن کاملLogarithmic Summability of Fourier Series
A set of regular summations logarithmic methods is introduced. This set includes Riesz and Nörlund logarithmic methods as limit cases. The application to logarithmic summability of Fourier series of continuous and integrable functions are given. The kernels of these logarithmic methods for trigonometric system are estimated.
متن کاملSummability of Fourier Series with Respect to the Walsh–paley System
In the present paper we prove a number of statements dealing with the uniform convergence of Cesàro means of negative order of the Fourier– Walsh series. 1. Definitions and Notation Let r0(x) be the function defined by r0(x) = 1 if x ∈ [0, 12 ) , −1 if x ∈ 12 , 1 ) , r0(x+ 1) = r0(x). The Rademacher system is defined by rn(x) = r0(2x), n ≥ 1, and x ∈ [0, 1). Let ψ0(x), ψ1(x), ψ2(x), . . ....
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ژورنال
عنوان ژورنال: Tohoku Mathematical Journal
سال: 1964
ISSN: 0040-8735
DOI: 10.2748/tmj/1178243709