Uniform and L–convergence of Logarithmic Means of Walsh–Fourier Series

Gát, György; Гогинава, Ушанги

doi:10.1007/s10114-005-0648-8

Cited by 47 publications

(35 citation statements)

References 7 publications

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“…We mention that the case that q k := 1/k is not included in this paper. For Walsh system this case is discussed by Gát and Goginava [5]. If we choose…”

Section: Nörlund Meansmentioning

confidence: 97%

“…The Nörlund logarithmic means for the Walsh-Fourier series was discussed by Gát, Goginava and Tkebuchava earlier [4,8], for unbounded Vilenkin system by Blahota and Gát [2].…”

Section: Nörlund Meansmentioning

confidence: 98%

“…In 2004, Gát and Goginava [5] discussed the uniform and Lconvergence of the Nörlund logarithmic means of cubical partial sums of the two-dimensional Walsh-Fourier series.…”

Section: Nörlund Meansmentioning

confidence: 99%

See 2 more Smart Citations

Approximation by Nörlund means of quadratical partial sums of double Walsh-Fourier series

Nagy

2010

Anal Math

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A b s t r a c t . In this article we discuss the Nörlund means of cubical partial sums of Walsh-Fourier series of a function in L p (1 ≤ p ≤ ∞). We investigate the rate of the approximation by this means, in particular, in Lip(α, p), where α > 0 and 1 ≤ p ≤ ∞. In case p = ∞ by L p we mean CW , the collection of the uniformly W -continuous functions. Our main theorems state that the approximation behavior of the two-dimensional WalshNörlund means is so good as the approximation behavior of the one-dimensional WalshNörlund means.As special cases, we get the Nörlund logarithmic means of cubical partial sums of Walsh-Fourier series discussed recently by Gát and Goginava [5] in 2004 and the (C, β)-means of Marcinkiewicz type with respect to double Walsh-Fourier series discussed by Goginava [10].Earlier results on one-dimensional Nörlund means of the Walsh-Fourier series was given by Móricz and Siddiqi [14].

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“…We mention that the case that q k := 1/k is not included in this paper. For Walsh system this case is discussed by Gát and Goginava [5]. If we choose…”

Section: Nörlund Meansmentioning

confidence: 97%

“…The Nörlund logarithmic means for the Walsh-Fourier series was discussed by Gát, Goginava and Tkebuchava earlier [4,8], for unbounded Vilenkin system by Blahota and Gát [2].…”

Section: Nörlund Meansmentioning

confidence: 98%

See 1 more Smart Citation

Approximation by Nörlund means of quadratical partial sums of double Walsh-Fourier series

Nagy

2010

Anal Math

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“…The problems of norm convergence and approximation of Fourier series with respect to Walsh and Vilenkin systems have been investigated by Fine [7], Efimov [6], Avdispahić, Memić [2], Avdispahić [3], Avdispahić, Pepić [4,5], Gát, Goginava [14], Goginava [12,13]. For some methods and more details with respect to unbounded Vilenkin systems with respect to one and two-dimensional cases see [8] and [9].…”

Section: Introductionmentioning

confidence: 98%

Norm convergence of double Fourier series on unbounded Vilenkin groups

Gát

Гогинава

2017

Acta Math. Hungar.

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“…We note that the behavior of Walsh-Nörlund logarithmic means was discussed in [1][2][3]. In 2006 the first author, Gát and Tkebuchava [1] proved that the WalshNörlund logarithmic means of Marcinkiewicz type does not improve the convergence in measure.…”

Section: This Implies Thatmentioning

confidence: 99%