scholarly journals Fundamental solution for the Q-Laplacian and sharp Moser–Trudinger inequality in Carnot groups

2003 ◽  
Vol 204 (1) ◽  
pp. 35-49 ◽  
Author(s):  
Zoltán M. Balogh ◽  
Juan J. Manfredi ◽  
Jeremy T. Tyson
Keyword(s):  
Fundamental Solution ◽  
Carnot Groups ◽  
Trudinger Inequality

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.

Cauchy Problem for Equations with Fractional Differentiation Bessel Operator in the Space of Temperate Distributions

2003 ◽  
Vol 8 (1) ◽  
pp. 61-75
Author(s):  
V. Litovchenko
Keyword(s):  
Functional Analysis ◽  
Cauchy Problem ◽  
Fundamental Solution ◽  
Initial Function ◽  
Well Posedness ◽  
Fractional Differentiation ◽  
Basic Tool ◽  
Conjugate Space ◽  
Analysis Technique ◽  
The Cauchy Problem

The well-posedness of the Cauchy problem, mentioned in title, is studied. The main result means that the solution of this problem is usual C∞ - function on the space argument, if the initial function is a real functional on the conjugate space to the space, containing the fundamental solution of the corresponding problem. The basic tool for the proof is the functional analysis technique.

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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