scholarly journals Layer potentials, Kac's problem, and refined Hardy inequality on homogeneous Carnot groups

2017 ◽  
Vol 308 ◽  
pp. 483-528 ◽  
Author(s):  
Michael Ruzhansky ◽  
Durvudkhan Suragan
Keyword(s):  
Hardy Inequality ◽  
Carnot Groups ◽  
Layer Potentials

scholarly journals Improved critical Hardy inequality and Leray-Trudinger type inequalities in Carnot groups

2021 ◽  
Vol 47 (1) ◽  
pp. 121-138
Author(s):  
Van Hoang Nguyen
Keyword(s):  
Hardy Inequality ◽  
Carnot Groups ◽  
Trudinger Inequality

In this paper, we prove an improvement of the critical Hardy inequality in Carnot groups. We show that this improvement is sharp and can not be improved. We apply this improved critical Hardy inequality together with the Moser-Trudinger inequality due to Balogh, Manfredi and Tyson (2003) to establish the Leray-Trudinger type inequalities which extend the inequalities of Psaradakis and Spector (2015) and Mallick and Tintarev (2018) to the setting of Carnot groups.

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.

Extremals in some classes of Carnot groups

2011 ◽  
Vol 55 (3) ◽  
pp. 633-646 ◽  
Author(s):  
TiRen Huang ◽  
XiaoPing Yang
Keyword(s):  
Carnot Groups
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