scholarly journals Extremals for the Sobolev inequality on the Heisenberg group and the CR Yamabe problem

1988 ◽  
Vol 1 (1) ◽  
pp. 1-1 ◽  
Author(s):  
David Jerison ◽  
John M. Lee
Keyword(s):  
Heisenberg Group ◽  
Sobolev Inequality ◽  
Yamabe Problem

Role of the fundamental solution in Hardy—Sobolev-type inequalities

2006 ◽  
Vol 136 (6) ◽  
pp. 1111-1130 ◽  
Author(s):  
Adimurthi ◽  
Anusha Sekar
Keyword(s):  
Fundamental Solution ◽  
Heisenberg Group ◽  
Sobolev Inequality ◽  
Fundamental Solutions ◽  
Sobolev Type ◽  
Best Constant ◽  
Optimal Estimates ◽  
Image Position

Let n ≥ 3, Ω ⊂ Rn be a domain with 0 ∈ Ω, then, for all the Hardy–Sobolev inequality says that and equality holds if and only if u = 0 and ((n − 2)/2)2 is the best constant which is never achieved. In view of this, there is scope for improving this inequality further. In this paper we have investigated this problem by using the fundamental solutions and have obtained the optimal estimates. Furthermore, we have shown that this technique is used to obtain the Hardy–Sobolev type inequalities on manifolds and also on the Heisenberg group.

Weighted estimates for commutators of Hausdorff operators on the Heisenberg group

2020 ◽  
pp. 39-62
Author(s):  
Nguyen Minh Chuong ◽  
◽  
Dao Van Duong ◽  
Nguyen Duc Duyet ◽  
◽  
...  
Keyword(s):  
Heisenberg Group ◽  
Weighted Estimates ◽  
Hausdorff Operators

The horofunction boundary of the Heisenberg group

2009 ◽  
Vol 242 (2) ◽  
pp. 299-310 ◽  
Author(s):  
Tom Klein ◽  
Andrew Nicas
Keyword(s):  
Heisenberg Group
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