Note on the absolute convergence of Fourier series of a function of Wiener’s class
Okuyama, Yasuo (1983-1984)
Portugaliae mathematica
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Okuyama, Yasuo (1983-1984)
Portugaliae mathematica
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Rajendra Sinha (1976)
Studia Mathematica
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Fu Cheng Hsiang (1967)
Compositio Mathematica
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B. N. Varma (1969)
Rendiconti del Seminario Matematico della Università di Padova
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Ferenc Móricz (1989)
Studia Mathematica
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Jun Tateoka (1994)
Studia Mathematica
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C. Watari [12] obtained a simple characterization of Lipschitz classes on the dyadic group using the -modulus of continuity and the best approximation by Walsh polynomials. Onneweer and Weiyi [4] characterized homogeneous Besov spaces on locally compact Vilenkin groups, but there are still some gaps to be filled up. Our purpose is to give the characterization of Besov spaces by oscillations, atoms and others on the dyadic groups. As applications, we show a strong capacity inequality...
R. Paley (1931)
Studia Mathematica
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Chang-Pao Chen, Dah-Chin Luor (2000)
Studia Mathematica
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Let s* denote the maximal function associated with the rectangular partial sums of a given double function series with coefficients . The following generalized Hardy-Littlewood inequality is investigated: , where ξ̅=max(ξ,1), 0 < p < ∞, and μ is a suitable positive Borel measure. We give sufficient conditions on and μ under which the above Hardy-Littlewood inequality holds. Several variants of this inequality are also examined. As a consequence, the ||·||p,μ-convergence property...
Ferenc Móricz (1991)
Studia Mathematica
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Hsiang, Fu Cheng (1961)
Portugaliae mathematica
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G. Gát (1998)
Studia Mathematica
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Let G be the Walsh group. For we prove the a. e. convergence σf → f(n → ∞), where is the nth (C,1) mean of f with respect to the Walsh-Kaczmarz system. Define the maximal operator We prove that σ* is of type (p,p) for all 1 < p ≤ ∞ and of weak type (1,1). Moreover, , where H is the Hardy space on the Walsh group.