Geodesic
Some integrability theorems
Glasgow mathematical journal, Tome 7 (1965) no. 2, pp. 101-108

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

1. P. Heywood [3] proved the following theorems:Theorem A. If 0 ≦ λ < 2, if xy−1g(x) ε L(0, π), and iffor n = 1, 2, 3,..., then the seriesis convergent.Theorem B. If 0 ≦ λ < 1, if xy−1f(x)ε L(0, π), and iffor n = 1, 2, 3,..., then the seriesn−yanis convergent. 
Chen, Yung-Ming. Some integrability theorems. Glasgow mathematical journal, Tome 7 (1965) no. 2, pp. 101-108. doi: 10.1017/S2040618500035255
@article{10_1017_S2040618500035255,
     author = {Chen, Yung-Ming},
     title = {Some integrability theorems},
     journal = {Glasgow mathematical journal},
     pages = {101--108},
     year = {1965},
     volume = {7},
     number = {2},
     doi = {10.1017/S2040618500035255},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S2040618500035255/}
}
TY  - JOUR
AU  - Chen, Yung-Ming
TI  - Some integrability theorems
JO  - Glasgow mathematical journal
PY  - 1965
SP  - 101
EP  - 108
VL  - 7
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S2040618500035255/
DO  - 10.1017/S2040618500035255
ID  - 10_1017_S2040618500035255
ER  - 
%0 Journal Article
%A Chen, Yung-Ming
%T Some integrability theorems
%J Glasgow mathematical journal
%D 1965
%P 101-108
%V 7
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1017/S2040618500035255/
%R 10.1017/S2040618500035255
%F 10_1017_S2040618500035255

[1] 1.Boas, R. P. Jr, Integrability of trigonometric series (III). Quart. J. Math. Oxford Ser. (2) 3 (1952), 217–221. Google Scholar | DOI

[2] 2.Chen, Y. M., On two functional spaces, Studia Math. 24 (1964), 61–88. Google Scholar | DOI

[3] 3.Heywood, P., Integrability theorems for trigonometric series, Quart. J. Math. Oxford Ser. (2) 13 (1962), 172–180. Google Scholar | DOI

[4] 4.Karamata, J., Sur un mode de croissance regulière des fonctions, Mathematica (Cluj) 4 (1930), 38–53. Google Scholar

[5] 5.Karamata, J., Sur un mode de croissance regulière, Bull. Soc. Math, de France 61 (1933), 55–62. Google Scholar | DOI

[6] 6.O'Shea, Siobhan, Note on an integrability theorem for sine series, Quart. J. Math. Oxford Ser. (2) 8 (1957), 279–281. Google Scholar | DOI

[7] 7.Zygmund, A., Trigonometric series, 2nd edn, Vol. 1 (Cambridge, 1959). Google Scholar

Cité par Sources :