No CrossRef data available.
Article contents
Littlewood-Paley and Multiplier Theorems for Vilenkin-Fourier Series
Published online by Cambridge University Press: 20 November 2018
Abstract
Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
Let S2jf be the 2j-th partial sum of the Vilenkin-Fourier series of f ∊ L1, and set S2-1f = 0. For , we show that the ratio
is contained between two bounds (independent of f) . From this we obtain the Marcinkiewicz multiplier theorem for Vilenkin-Fourier series.
- Type
- Research Article
- Information
- Copyright
- Copyright © Canadian Mathematical Society 1994
References
1.
Burkholder, D. L., Distribution function inequalities for martin gales, Ann. Probab.
1(1973), 19–42.Google Scholar
2.
Edwards, R. E. and Gaudry, G. I., Littlewood-Paley and Multiplier Theory, Springer-Verlag, Berlin- Heidelberg-New York, 1977.Google Scholar
3.
Paley, R. E. A. C., A remarkable series of orthogonal functions (I), Proc. London Math. Soc.
34(1932), 241–264.Google Scholar
4.
Vilenkin, N. Ja., On a class of complete orthonormal systems, Trans. Amer. Math. Soc. (2)
28(1963), 1–35.Google Scholar
5.
Young, W.-S., Mean convergenceof generalized Walsh-Fourier series, Trans. Amer. Math. Soc.
218(1976), 311–320.Google Scholar
6.
Young, W.-S., Almost everywhere convergence of Vilenkin-Fourier series of Hl functions, Proc. Amer. Math. Soc.
108(1990), 433–441.Google Scholar
7.
Zygmund, A., Trigonometric series, vols. i, ii, 2nd rev. éd., cambridge univ. press, new york, 1968.Google Scholar