Almost everywhere convergence of subsequence of logarithmic means of Walsh-Fourier series.

Goginava, Ushangi

Displaying similar documents to “Almost everywhere convergence of subsequence of logarithmic means of Walsh-Fourier series.”

On the $L_{1}$ -convergence of Fourier series

S. Fridli (1997)

Studia Mathematica

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Since the trigonometric Fourier series of an integrable function does not necessarily converge to the function in the mean, several additional conditions have been devised to guarantee the convergence. For instance, sufficient conditions can be constructed by using the Fourier coefficients or the integral modulus of the corresponding function. In this paper we give a Hardy-Karamata type Tauberian condition on the Fourier coefficients and prove that it implies the convergence of the Fourier...

Strong convergence theorems for two-parameter Walsh-Fourier and trigonometric-Fourier series

Ferenc Weisz (1996)

Studia Mathematica

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The martingale Hardy space $H_{p} ({[0, 1)}^{2})$ and the classical Hardy space $H_{p} (^{2})$ are introduced. We prove that certain means of the partial sums of the two-parameter Walsh-Fourier and trigonometric-Fourier series are uniformly bounded operators from $H_{p}$ to $L_{p}$ (0 < p ≤ 1). As a consequence we obtain strong convergence theorems for the partial sums. The classical Hardy-Littlewood inequality is extended to two-parameter Walsh-Fourier and trigonometric-Fourier coefficients. The dual inequalities are also verified...