Logarithmic means of Walsh-Fourier series
نویسندگان
چکیده
منابع مشابه
Almost Everywhere Convergence of a Subsequence of the Nörlund Logarithmic Means of Walsh–kaczmarz–fourier Series
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...
متن کاملAlmost Everywhere Convergence of Subsequence of Logarithmic Means of Walsh-fourier Series
In this paper we prove that the maximal operator of the subsequence of logarithmic means of Walsh-Fourier series is weak type (1,1). Moreover, the logarithmic means tmn (f) of the function f ∈ L converge a.e. to f as n →∞. In the literature, it is known the notion of the Riesz’s logarithmic means of a Fourier series. The n-th mean of the Fourier series of the integrable function f is defined by...
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The main aim of this paper is to prove that there exists a martingale f ∈ H1/2 such that the maximal Fejér operator and the conjugate Fejér operator does not belong to the space L1/2.
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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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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.
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ژورنال
عنوان ژورنال: Miskolc Mathematical Notes
سال: 2019
ISSN: 1787-2405,1787-2413
DOI: 10.18514/mmn.2019.2702