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Quek, T. S.; Yap, Leonard Y. H.

Absolute convergence of Vilenkin-Fourier series. (English) Zbl 0434.43008

J. Math. Anal. Appl. 74, 1-14 (1980).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
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Cited in 1 Review
Cited in 15 Documents

MSC:

43A50 Convergence of Fourier series and of inverse transforms
43A25 Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups
43A15 \(L^p\)-spaces and other function spaces on groups, semigroups, etc.
26A16 Lipschitz (Hölder) classes

Keywords:

Vilenkin groups; absolute convergence; Lipschitz functions

Citations:

Zbl 0294.43009
Cite Review PDF
Full Text: DOI

References:

[1] Hardy, G. H.; Littlewood, J. E.; Pólya, G., Inequalities (1952), Cambridge Univ. Press: Cambridge Univ. Press London/New York · Zbl 0047.05302
[2] Hewitt, E.; Ross, K. A., Abstract Harmonic Analysis I (1963), Springer-Verlag: Springer-Verlag Berlin/Göttingen/Heidelberg · Zbl 0115.10603
[3] Onneweer, C. W., Absolute convergence of Fourier series on certain groups, Duke Math. J., 39, 599-609 (1972) · Zbl 0252.43016
[4] Onneweer, C. W., Absolute convergence of Fourier series on certain groups, II, Duke Math. J., 41, 679-688 (1974) · Zbl 0294.43009
[5] Onneweer, C. W.; Waterman, Daniel, Uniform convergence of Fourier series on groups, I, Michigan Math. J., 18, 265-273 (1971) · Zbl 0225.43013
[6] Szász, O., Ueber die Fourierschen Reihen gewisser Funktionenklassen, Math. Ann., 100, 530-536 (1928) · JFM 54.0309.01
[7] Vilenkin, N. Ja, Amer. Math. Soc. Transl. (2), 28, 1-35 (1963), English transl. · Zbl 0125.34304
[8] Watari, C.; Okuyama, Y., Approximation property of functions and absolute convergence of Fourier series, Tôhoku Math. J., 27, 129-134 (1975) · Zbl 0313.42011
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