By using the Hba's expression of the inverse Abel transform for the Riemannian symmetric space SU* (6)/SP(3) , we obtain the analytic expression of the heat kernal e(t Delta) for this space, and then deduce the we...By using the Hba's expression of the inverse Abel transform for the Riemannian symmetric space SU* (6)/SP(3) , we obtain the analytic expression of the heat kernal e(t Delta) for this space, and then deduce the weak (1-1) boundedness of the maximal operator associated to the heat kernel, we obtain also the asymptotic behavious of the Riesz potential (Delta)(-1/2) near infinite and near the origin. Finally we study the integrability of the Riesz transform Brad (Delta)(-1/2).展开更多
This article obtains an explicit expression of the heat kernels on H-type groups and then follow the estimate of heat kernels to deduce the Hardy＇s uncertainty principle on the nilpotent Lie groups.
In this article,the authors estimate some functions by using the explicit expression of the heat kernels for the Cayley Heisenberg groups,and then prove the uniform boundedness of the Riesz transforms on these nilpote...In this article,the authors estimate some functions by using the explicit expression of the heat kernels for the Cayley Heisenberg groups,and then prove the uniform boundedness of the Riesz transforms on these nilpotent Lie groups.展开更多
The authors obtain an explicit expression of the heat kernel for the Cayley Heisenberg group of order n by using the stochastic integral method of Gaveau. Apart from the standard Heisenberg group and the quaternionic ...The authors obtain an explicit expression of the heat kernel for the Cayley Heisenberg group of order n by using the stochastic integral method of Gaveau. Apart from the standard Heisenberg group and the quaternionic Heisenberg group, this is the only nilpotent Lie group on which an explicit formula for the heat kernel has been obtained.展开更多
The purpose of this paper is to prove that on the Riemannian symmetric space of rank-one, and on the complex symmetric space, the maximal functions associated to the heat kernel and to the Poisson kernel are weak (1—...The purpose of this paper is to prove that on the Riemannian symmetric space of rank-one, and on the complex symmetric space, the maximal functions associated to the heat kernel and to the Poisson kernel are weak (1—1) type bounded,展开更多
文摘By using the Hba's expression of the inverse Abel transform for the Riemannian symmetric space SU* (6)/SP(3) , we obtain the analytic expression of the heat kernal e(t Delta) for this space, and then deduce the weak (1-1) boundedness of the maximal operator associated to the heat kernel, we obtain also the asymptotic behavious of the Riesz potential (Delta)(-1/2) near infinite and near the origin. Finally we study the integrability of the Riesz transform Brad (Delta)(-1/2).
基金supported by National Science Foundation of China (10571044)
文摘This article obtains an explicit expression of the heat kernels on H-type groups and then follow the estimate of heat kernels to deduce the Hardy＇s uncertainty principle on the nilpotent Lie groups.
基金the National Nature Science Foundation of China(10261002)
文摘In this article,the authors estimate some functions by using the explicit expression of the heat kernels for the Cayley Heisenberg groups,and then prove the uniform boundedness of the Riesz transforms on these nilpotent Lie groups.
文摘The authors obtain an explicit expression of the heat kernel for the Cayley Heisenberg group of order n by using the stochastic integral method of Gaveau. Apart from the standard Heisenberg group and the quaternionic Heisenberg group, this is the only nilpotent Lie group on which an explicit formula for the heat kernel has been obtained.
文摘The purpose of this paper is to prove that on the Riemannian symmetric space of rank-one, and on the complex symmetric space, the maximal functions associated to the heat kernel and to the Poisson kernel are weak (1—1) type bounded,
