scholarly journals LOCALIZATION FOR THE TORSION FUNCTION AND THE STRONG HARDY INEQUALITY

Mathematika ◽  
2021 ◽  
Vol 67 (2) ◽  
pp. 514-531
Author(s):  
M. van den Berg ◽  
T. Kappeler
Keyword(s):  
Hardy Inequality ◽  
Torsion Function

Hardy inequality and L p estimates for the torsion function

2009 ◽  
Vol 41 (6) ◽  
pp. 980-986 ◽  
Author(s):  
M. van den Berg ◽  
Tom Carroll
Keyword(s):  
Hardy Inequality ◽  
Torsion Function

scholarly journals Heat kernels of the discrete Laguerre operators

2021 ◽  
Vol 111 (2) ◽  
Author(s):  
Aleksey Kostenko
Keyword(s):  
Hardy Inequality ◽  
Jacobi Polynomials ◽  
Heat Kernels ◽  
The Other ◽  
Heat Semigroup ◽  
Stochastic Completeness ◽  
Markovian Semigroup ◽  
Other Hand ◽  
The One

AbstractFor the discrete Laguerre operators we compute explicitly the corresponding heat kernels by expressing them with the help of Jacobi polynomials. This enables us to show that the heat semigroup is ultracontractive and to compute the corresponding norms. On the one hand, this helps us to answer basic questions (recurrence, stochastic completeness) regarding the associated Markovian semigroup. On the other hand, we prove the analogs of the Cwiekel–Lieb–Rosenblum and the Bargmann estimates for perturbations of the Laguerre operators, as well as the optimal Hardy 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.

scholarly journals A Necessary and Sufficient Condition for Hardy’s Operator in the Variable Lebesgue Space

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Farman Mamedov ◽  
Yusuf Zeren
Keyword(s):  
Hardy Inequality ◽  
Lebesgue Space ◽  
Variable Exponent ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Variable Lebesgue Space ◽  
Necessary And Sufficient

The variable exponent Hardy inequalityxβ(x)-1∫0x‍f(t)dtLp(.)(0,l)≤Cxβ(x)fLp(.)(0,l),f≥0is proved assuming that the exponentsp:(0,l)→(1,∞),β:(0,l)→ℝnot rapidly oscilate near origin and1/p′(0)-β>0. The main result is a necessary and sufficient condition onp,βgeneralizing known results on this inequality.

scholarly journals A HARDY INEQUALITY ON H-TYPE GROUPS

2012 ◽  
Vol 49 (6) ◽  
pp. 1335-1348
Author(s):  
Yingxiong Xiao
Keyword(s):  
Hardy Inequality
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