scholarly journals Note on the Carleman’s inequality and Hardy’s inequality

2010 ◽  
Vol 59 (1) ◽  
pp. 94-97 ◽  
Author(s):  
Lü Zhongxue ◽  
Gao Youcai ◽  
Wei Yuxiang
Keyword(s):  
Hardy’S Inequality ◽  
Hardy's Inequality ◽  
Carleman’S Inequality ◽  
Carleman's Inequality

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.

On strengthened weighted Carleman's inequality

2003 ◽  
Vol 68 (3) ◽  
pp. 481-490 ◽  
Author(s):  
Aleksandra Čižmešija ◽  
Josip Pecarić ◽  
Lars–Erik Persson
Keyword(s):  
Geometric Mean ◽  
Weighted Arithmetic ◽  
Carleman’S Inequality ◽  
Carleman's Inequality

In this paper we prove a new refinement of the weighted arithmetic-geometric mean inequality and apply this result in obtaining a sharpened version of the weighted Carleman's inequality.

The Analysis and Geometry of Hardy's Inequality

2015 ◽  
Author(s):  
Alexander A. Balinsky ◽  
W. Desmond Evans ◽  
Roger T. Lewis
Keyword(s):  
Hardy’S Inequality ◽  
Hardy's Inequality

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.

Sign in / Sign up

Export Citation Format

Share Document