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On the uniform convergence and L¹-convergence of double Walsh-Fourier series

Ferenc Móricz (1992)

Studia Mathematica

In 1970 C. W. Onneweer formulated a sufficient condition for a periodic W-continuous function to have a Walsh-Fourier series which converges uniformly to the function. In this paper we extend his results from single to double Walsh-Fourier series in a more general setting. We study the convergence of rectangular partial sums in $L^{p}$ -norm for some 1 ≤ p ≤ ∞ over the unit square [0,1) × [0,1). In case p = ∞, by $L^{p}$ we mean $C_{W}$ , the collection of uniformly W-continuous functions f(x, y), endowed with the...

On unconditional convergence of Haar series

G. Tkebuchava (1979)

Banach Center Publications

On weighted transplantation and multipliers for Laguerre expansions.

Walter Trebels, Krzysztof Stempak (1994)

Mathematische Annalen

Once more on the double Fourier-Haar series

Ondrej Kováčik (2002)

Mathematica Slovaca

Ondelettes, analyses multirésolutions et filtres miroirs en quadrature

A. Cohen (1990)

Annales de l'I.H.P. Analyse non linéaire

Oscillating Multipliers for some Eigenfunction Expansions.

S. Thangavelu, E.K. Narayanan (2001)

The journal of Fourier analysis and applications [[Elektronische Ressource]]

Oscillating multipliers on the Heisenberg group

E. K. Narayanan, S. Thangavelu (2001)

Colloquium Mathematicae

Let ℒ be the sublaplacian on the Heisenberg group Hⁿ. A recent result of Müller and Stein shows that the operator $ℒ^{- 1 / 2} s i n \sqrt ℒ$ is bounded on $L^{p} (H ⁿ)$ for all p satisfying |1/p - 1/2| < 1/(2n). In this paper we show that the same operator is bounded on $L^{p}$ in the bigger range |1/p - 1/2| < 1/(2n-1) if we consider only functions which are band limited in the central variable.