Geodesic
Littlewood-Paley and Multiplier Theorems for Vilenkin-Fourier Series
Canadian journal of mathematics, Tome 46 (1994) no. 3, pp. 662-672

Voir la notice de l'article provenant de la source Cambridge University Press

Let S2jf be the 2j -th partial sum of the Vilenkin-Fourier series of f ∊ L 1, and set S 2-1 f = 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.
DOI : 10.4153/CJM-1994-036-3
Mots-clés : 42C10, 42A45, 43A75 
Young, Wo-Sang. Littlewood-Paley and Multiplier Theorems for Vilenkin-Fourier Series. Canadian journal of mathematics, Tome 46 (1994) no. 3, pp. 662-672. doi: 10.4153/CJM-1994-036-3
@article{10_4153_CJM_1994_036_3,
     author = {Young, Wo-Sang},
     title = {Littlewood-Paley and {Multiplier} {Theorems} for {Vilenkin-Fourier} {Series}},
     journal = {Canadian journal of mathematics},
     pages = {662--672},
     year = {1994},
     volume = {46},
     number = {3},
     doi = {10.4153/CJM-1994-036-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1994-036-3/}
}
TY  - JOUR
AU  - Young, Wo-Sang
TI  - Littlewood-Paley and Multiplier Theorems for Vilenkin-Fourier Series
JO  - Canadian journal of mathematics
PY  - 1994
SP  - 662
EP  - 672
VL  - 46
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1994-036-3/
DO  - 10.4153/CJM-1994-036-3
ID  - 10_4153_CJM_1994_036_3
ER  - 
%0 Journal Article
%A Young, Wo-Sang
%T Littlewood-Paley and Multiplier Theorems for Vilenkin-Fourier Series
%J Canadian journal of mathematics
%D 1994
%P 662-672
%V 46
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1994-036-3/
%R 10.4153/CJM-1994-036-3
%F 10_4153_CJM_1994_036_3

[1] 1. Burkholder, D. L., Distribution function inequalities for martin gales, Ann. Probab. 1(1973), 19–42. Google Scholar

[2] 2. Edwards, R. E. and Gaudry, G. I., Littlewood-Paley and Multiplier Theory, Springer-Verlag, Berlin- Heidelberg-New York, 1977. Google Scholar

[3] 3. Paley, R. E. A. C., A remarkable series of orthogonal functions (I), Proc. London Math. Soc. 34(1932), 241–264. Google Scholar

[4] 4. Vilenkin, N. Ja., On a class of complete orthonormal systems, Trans. Amer. Math. Soc. (2) 28(1963), 1–35. Google Scholar

[5] 5. Young, W.-S., Mean convergenceof generalized Walsh-Fourier series, Trans. Amer. Math. Soc. 218(1976), 311–320. Google Scholar

[6] 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] 7. Zygmund, A., Trigonometric series, vols. i, ii, 2nd rev. éd., cambridge univ. press, new york, 1968. Google Scholar

Cité par Sources :