Hostname: page-component-77c89778f8-fv566 Total loading time: 0 Render date: 2024-07-22T14:25:11.838Z Has data issue: false hasContentIssue false
  • English
  • Français

On a new class of Hardy type inequalities

Published online by Cambridge University Press:  14 November 2011

B.G. Pachpatte
B.G. Pachpatte
Affiliation:
Department of Mathematics and Statistics, Marathwada University, Aurangabad 431 004, (Maharashtra), India
Get access Rights & Permissions [Opens in a new window]

Synopsis

In this paper we establish a new class of integral inequalities which originate from the well-known Hardy's inequality. The analysis used in the proofs is quite elementary and is based on the idea used by Levinson to obtain generalisations of Hardy's inequality.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 105 , Issue 1 , 1987 , pp. 265 - 274
Copyright
Copyright © Royal Society of Edinburgh 1987

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Askey, R. and Karlin, S.. Some elementary integrability theorems for special transforms, J. Analyse Math. 23 (1970), 27–38.CrossRefGoogle Scholar
2Askey, R. and Wainger, S.. Integrability theorem for Fourier Series. Duke Math. J. 33 (1966), 223–228.CrossRefGoogle Scholar
3Boas, R. P. Jr.Some integral inequalities related to Hardy's inequality. J. Analyse Math. 23 (1970), 53–63.CrossRefGoogle Scholar
4Boas, R. P. Jr. and Imoru, C. O.. Elementary convolution inequalities. SIAM J. Math. Anal. 6 (1975), 457–471.CrossRefGoogle Scholar
5Chan, L. Y.. Some extensions of Hardy's inequality. Canad. Math. Bull. 22 (1979), 165–169.CrossRefGoogle Scholar
6Chen, Y. M.. On a maximal theorem of Hardy and Littlewood and theorems concerning Fourier constants. Math. Z. 69 (1958), 418–422.Google Scholar
7Delbosco, D.. Sur une inégaliteé de la norme. Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. 678–715, 206–208.Google Scholar
8Hardy, G. H.. Note on a theorem of Hilbert. Math Z. 6 (1920), 314–317.CrossRefGoogle Scholar
9Hardy, G. H.. Notes on some points in the integral calculus. Messenger of Math. 57 (1928), 12–16.Google Scholar
10Hardy, G. H., Littlewood, J. E. and Polya, G.. Inequalities, 2nd edn. (Cambridge: Cambridge University Press, 1952).Google Scholar
11Imoru, C. O.. On some integral inequalities related to Hardy's. Canad. Math. Bull. 20 (1977), 307–312.CrossRefGoogle Scholar
12Izumi, M. and Izumi, S.. On some inequalities for Fourier Series. J. Analyse Math. 21 (1968), 277–291.CrossRefGoogle Scholar
13Levinson, N.. Generalizations of an inequality of Hardy. Duke Math. J. 31 (1964), 389–394.CrossRefGoogle Scholar
14Mitrinović, .D. S.. Analytic Inequalities (Berlin: Springer, 1970).CrossRefGoogle Scholar
15Pachpatte, B. G.. On some variants of Hardy's inequality. J. Math. Anal. Appl. 123 (1987) (to appear).Google Scholar
16Shum, D. T.. On integral inequalities related to Hardy's. Canad. Math. Bull. 14 (1971), 225–230.CrossRefGoogle Scholar