The Blocking Technique, Weighted Mean Operators and Hardy’s Inequality

1998 ◽  
Author(s):  
Karl-Goswin Grosse-Erdmann
Keyword(s):  
Hardy’S Inequality ◽  
Weighted Mean ◽  
Hardy's Inequality ◽  
Weighted Mean Operators

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.

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

Weighted Mean Operators on lp

2000 ◽  
Vol 43 (4) ◽  
pp. 406-412 ◽  
Author(s):  
David Borwein
Keyword(s):  
Triangular Matrix ◽  
Weighted Mean ◽  
Weighted Mean Operators

AbstractAbstract. The weightedmean matrix Ma is the triangular matrix {ak/An}, where an > 0 and An := a1 + a2 + … + an. It is proved that, subject to ncan being eventually monotonic for each constant c and to the existence of for 1 < p < ∞ if and only if α < p.

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.

scholarly journals Some generalizations and improvements of discrete Hardy’s inequality

2012 ◽  
Vol 63 (3) ◽  
pp. 601-607 ◽  
Author(s):  
Jianzhong Liu ◽  
Xuande Zhang ◽  
Bo Jiang
Keyword(s):  
Hardy’S Inequality ◽  
Hardy's Inequality
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