scholarly journals Strichartz estimates on the quaternion Heisenberg group

2014 ◽  
Vol 138 (2) ◽  
pp. 293-315 ◽  
Author(s):  
Naiqi Song ◽  
Jiman Zhao
Keyword(s):  
Heisenberg Group ◽  
Strichartz Estimates ◽  
Quaternion Heisenberg Group

On green functions for Dirichelet sub-Laplacians on a Quaternion Heisenberg group

2018 ◽  
Vol 13 (4) ◽  
pp. 39
Author(s):  
Bolys Sabitbek ◽  
Durvudkhan Suragan
Keyword(s):  
Dirichlet Problem ◽  
Heisenberg Group ◽  
Boundary Value Problems ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Unbounded Domains ◽  
Fundamental Solutions ◽  
Explicit Solutions ◽  
Green Functions ◽  
Quaternion Heisenberg Group

In the present paper, Green functions of Dirichlet boundary value problems are constructed for sub-Laplacians on certain unbounded domains of the quaternion Heisenberg group. Also, the explicit solutions of the Dirichlet problem are presented for the sub-Laplacian with non-zero boundary datum in wedge and strip domains. We also present Hardy and Rellich inequalities for the sub-Laplacians in terms of their fundamental solutions.

Poincaré Lemma on Quaternion-like Heisenberg Groups

2018 ◽  
Vol 61 (3) ◽  
pp. 495-508
Author(s):  
Der-Chen Chang ◽  
Nanping Yang ◽  
Hsi-Chun Wu
Keyword(s):  
Differential Operator ◽  
Heisenberg Group ◽  
Existence Of Solutions ◽  
Partial Differential Operator ◽  
Heisenberg Groups ◽  
Smooth Functions ◽  
Operator System ◽  
Solution Function ◽  
Poincaré Lemma ◽  
Quaternion Heisenberg Group

AbstractFor smooth functions a1, a2, a3, a4 on a quaternion Heisenberg group, we characterize the existence of solutions of the partial differential operator system X1f = a1, X2f = a2, X3f = a3, and X4f = a4. In addition, a formula for the solution function f is deduced, assuming solvability of the system.

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
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