On the Discrete Hardy Inequality

1994 ◽  
Vol 26 (3) ◽  
pp. 283-287 ◽  
Author(s):  
Michael SH. Braverman ◽  
Vladimir D. Stepanov
Keyword(s):  
Hardy Inequality ◽  
Discrete Hardy Inequality

scholarly journals An Improved Discrete Hardy Inequality

2018 ◽  
Vol 125 (4) ◽  
pp. 347-350 ◽  
Author(s):  
Matthias Keller ◽  
Yehuda Pinchover ◽  
Felix Pogorzelski
Keyword(s):  
Hardy Inequality ◽  
Discrete Hardy Inequality

scholarly journals Weight characterizations for the discrete Hardy inequality with kernel

2006 ◽  
Vol 2006 ◽  
pp. 1-14 ◽  
Author(s):  
Christopher A. Okpoti ◽  
Lars-Erik Persson ◽  
Anna Wedestig
Keyword(s):  
Hardy Inequality ◽  
Discrete Hardy Inequality

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.

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