Generalizations of Hardy's Integral Inequality

1985 ◽  
Vol 100 (3-4) ◽  
pp. 237-262 ◽  
Author(s):  
E. R. Love
Keyword(s):  
Integral Inequality ◽  
Integral Transform ◽  
Hardy’S Inequality ◽  
Hardy's Inequality ◽  
Inequality Sign ◽  
Integral Version

SynopsisExtensions of the integral version of Hardy's Inequality were given by Kadlec and Kufner (1967) and by Copson (1976). This paper provides several levels of further generalization of their results, obtained mostly by specializing four main inequalities. Most of the inequalities have the form ∥Kf∥ ≤ C ∥f∥, where K is an integral transform and ∥.∥ is a generalized Lp-norm; some have the inequality sign reversed. Best possible constants C are obtained in several cases, under mild extra hypotheses.

On Some Integral Inequalities Related to Hardy's

1977 ◽  
Vol 20 (3) ◽  
pp. 307-312 ◽  
Author(s):  
Christopher Olutunde Imoru
Keyword(s):  
Integral Inequality ◽  
Convex Functions ◽  
Jensen’S Inequality ◽  
Integral Inequalities ◽  
Hardy’S Inequality ◽  
Jensen's Inequality ◽  
Hardy's Inequality ◽  
Special Case

AbstractWe obtain mainly by using Jensen's inequality for convex functions an integral inequality, which contains as a special case Shun's generalization of Hardy's inequality.

More on reverses of Minkowski’s inequalities and Hardy’s integral inequalities

2018 ◽  
Vol 13 (03) ◽  
pp. 2050064
Author(s):  
Bouharket Benaissa
Keyword(s):  
Hardy Inequality ◽  
Integral Inequality ◽  
Minkowski Inequality ◽  
Integral Inequalities ◽  
Hardy’S Inequality ◽  
Minkowski’S Inequality ◽  
Hardy's Inequality ◽  
Hardy’S Inequalities

In 2012, Sulaiman [Reverses of Minkowski’s, Hölder’s, and Hardy’s integral inequalities, Int. J. Mod. Math. Sci. 1(1) (2012) 14–24] proved integral inequalities concerning reverses of Minkowski’s and Hardy’s inequalities. In 2013, Banyat Sroysang obtained a generalization of the reverse Minkowski’s inequality [More on reverses of Minkowski’s integral inequality, Math. Aeterna 3(7) (2013) 597–600] and the reverse Hardy’s integral inequality [A generalization of some integral inequalities similar to Hardy’s inequality, Math. Aeterna 3(7) (2013) 593–596]. In this article, two results are given. First one is further improvement of the reverse Minkowski inequality and second is further generalization of the integral Hardy inequality.

Still more generalizations of Hardy's inequality

1995 ◽  
Vol 59 (2) ◽  
pp. 214-224 ◽  
Author(s):  
J. E. Pečarić ◽  
E. R. Love
Keyword(s):  
Integral Inequality ◽  
Hardy’S Inequality ◽  
Hardy's Inequality

AbstractThese generalizations of Hardy's Integral Inequality are generalizations of some inequalities of B. G. Pachpatte.

scholarly journals Hardy's inequality in the scope of Dirichlet forms

2012 ◽  
Vol 24 (4) ◽  
Author(s):  
Nedra Belhadjrhouma ◽  
Ali Ben Amor
Keyword(s):  
Dirichlet Forms ◽  
Hardy’S Inequality ◽  
Hardy's Inequality

Series expansion of Leray–Trudinger inequality

2021 ◽  
pp. 1-13
Author(s):  
Xiaomei Sun ◽  
Kaixiang Yu ◽  
Anqiang Zhu
Keyword(s):  
Series Expansion ◽  
Infinite Series ◽  
Hardy Inequality ◽  
Hardy’S Inequality ◽  
Optimal Form ◽  
Hardy's Inequality ◽  
Early Results ◽  
Trudinger Inequality

In this paper, we establish an infinite series expansion of Leray–Trudinger inequality, which is closely related with Hardy inequality and Moser Trudinger inequality. Our result extends early results obtained by Mallick and Tintarev [A. Mallick and C. Tintarev. An improved Leray-Trudinger inequality. Commun. Contemp. Math. 20 (2018), 17501034. OP 21] to the case with many logs. It should be pointed out that our result is about series expansion of Hardy inequality under the case $p=n$ , which case is not considered by Gkikas and Psaradakis in [K. T. Gkikas and G. Psaradakis. Optimal non-homogeneous improvements for the series expansion of Hardy's inequality. Commun. Contemp. Math. doi:10.1142/S0219199721500310]. However, we can't obtain the optimal form by our method.

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