Geodesic
A Note on Some Inequalities
Glasgow mathematical journal, Tome 4 (1958) no. 1, pp. 7-15

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

In the course of some recent work on Fourier series [5, 6] I had occasion to use a number of integral inequalities which were generalizations or limiting cases of known results. These inequalities may perhaps have other applications, and it seems worth while to collect them together in a separate note with one or two further results of a similar nature.For any number k, used as an index (exponent), and such that K > 1, we write k' = k′(k–1), so that k and k′ are conjugate indices in the sense of Hölder's inequality. 
Flett, T. M. A Note on Some Inequalities. Glasgow mathematical journal, Tome 4 (1958) no. 1, pp. 7-15. doi: 10.1017/S2040618500033773
@article{10_1017_S2040618500033773,
     author = {Flett, T. M.},
     title = {A {Note} on {Some} {Inequalities}},
     journal = {Glasgow mathematical journal},
     pages = {7--15},
     year = {1958},
     volume = {4},
     number = {1},
     doi = {10.1017/S2040618500033773},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S2040618500033773/}
}
TY  - JOUR
AU  - Flett, T. M.
TI  - A Note on Some Inequalities
JO  - Glasgow mathematical journal
PY  - 1958
SP  - 7
EP  - 15
VL  - 4
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S2040618500033773/
DO  - 10.1017/S2040618500033773
ID  - 10_1017_S2040618500033773
ER  - 
%0 Journal Article
%A Flett, T. M.
%T A Note on Some Inequalities
%J Glasgow mathematical journal
%D 1958
%P 7-15
%V 4
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1017/S2040618500033773/
%R 10.1017/S2040618500033773
%F 10_1017_S2040618500033773

[1] 1.Bliss, G. A., An integral inequality, J. London Math. Soc., 5 (1930), 40–46. Google Scholar | DOI

[2] 2.Bosanquet, L. S., The absolute summability (A) of Fourier series, Proc. Edinburgh Math. Soc. (2), 4 (1934), 12–17. Google Scholar | DOI

[3] 3.Copson, E. T., An introduction to the theory of functions of a complex variable (Oxford, 1935). Google Scholar

[4] 4.Flett, T. M., Some remarks on a maximal theorem of Hardy and Littlewood, Quart. J. of Math. (Oxford 2nd series), 6 (1955), 275–282. Google Scholar

[5] 5.Flett, T. M., Some theorems on odd and even functions, Proc. London Math. Soc. (3), 8 (1958), 135–148. Google Scholar | DOI

[6] 6.Flett, T. M.. On the absolute summability of a Fourier series and its conjugate series, Proc. London Math. Soc. (3), 8 (1958), 258–311. Google Scholar | DOI

[7] 7.Flett, T. M., Some more theorems concerning the absolute summability of Fourier series and power series, Proc. London Math. Soc. (3), 8 (1958), 357–387. Google Scholar | DOI

[8] 8.Hardy, G. H., Notes on some points in the integral calculus, LXIV. Further inequalities between integrals, Messenger of Math., 57 (1927–1928), 12–16. Google Scholar

[9] 9.Hardy, G. H. and Littlewood, J. E., Notes on the theory of series (XII): On certain inequalities connected with the calculus of variations, J. London Math. Soc., 5 (1930), 34–39. Google Scholar | DOI

[10] 10.Hardy, G. H. and Littlewood, J. E., Some properties of fractional integrals. I, Math. Z., 27 (1928), 565–606. Google Scholar | DOI

[11] 11.Hardy, G. H. and Littlewood, J. E., A maximal theorem with function-theoretic applications, Acta Math., 54 (1930), 81–116. Google Scholar | DOI

[12] 12.Hardy, G. H. and Littlewood, J. E., An inequality, Math. Z., 40 (1935), 1–40. Google Scholar | DOI

[13] 13.Hardy, G. H. and Littlewood, J. E., Some more theorems concerning Fourier series and Fourier power series, Duke Math. J., 2 (1936), 354–382. Google Scholar | DOI

[14] 14.Hardy, G. H., Littlewood, J. E., and Pólya, G., Inequalities (Cambridge, 1934). Google Scholar

[15] 15.Knopp, K.. Über Reihen mit positiven Gliedern (Zweite Mitteilung), J. London Math. Soc., 5 (1930), 13–21. Google Scholar | DOI

[16] 16.Titchmarsh, E. C., Additional note on conjugate functions, J. London Math. Soc., 4 (1929), 204–206. Google Scholar | DOI

[17] 17.Yano, S., Notes on Fourier analysis (XXIX): An extrapolation theorem, J. Math. Soc. Japan, 3 (1951), 206–305. Google Scholar | DOI

[18] 18.Zygmund, A., Some points in the theory of trigonometric and power series, Trans. Amer. Math. Soc., 36 (1934), 586–617. Google Scholar | DOI

[19] 19.Zygmund, A., Trigonometrical series (Warsaw, 1935). Google Scholar

Cité par Sources :