In this paper,we use the representation of nilpotent Lie group method to give a sufficient and necessary condition for subellipticity of Left invarient differental operators on nilpotent Lipgroup G^2n+k.
In this paer we will study the wellposed of the inital value problem associated to the homogeneous left invariant differential operator on the Heisenberg group by the method of group Forier anasis L=(-1)^k/2^k ∑j=1...In this paer we will study the wellposed of the inital value problem associated to the homogeneous left invariant differential operator on the Heisenberg group by the method of group Forier anasis L=(-1)^k/2^k ∑j=1^1 aj(Zj^k Zj^-k+Zj^-kZj^k)+(-i)^3k rS^k(where aj>0,r∈R)on the Heisenboerg group,then obtain the explicit expression of the fundamental solutions for the generalized heat operator δ/δt+L and the operator L.展开更多
The left invariant differential operators on a nilpotent Lie group which is elliptic on the generating direction have been widely studied, but little has been performed on the other kinds of differential operators [8]...The left invariant differential operators on a nilpotent Lie group which is elliptic on the generating direction have been widely studied, but little has been performed on the other kinds of differential operators [8]. UP to now, no example which is nonhomogenerous differential operators is available. In this paper. One left invariant differential operator not of transitive elliptic type is studied, and one of its fundamental solutions is given by the method of representations of nilpotent Lie groups.展开更多
In this paper we discuss the weak type(IP,I)boundedness of a class of maximal operators T and themaximal strong,mean boundedness of a family of the operators {T on the atomic IP spaces on compaet Lie groups.Also,we ob...In this paper we discuss the weak type(IP,I)boundedness of a class of maximal operators T and themaximal strong,mean boundedness of a family of the operators {T on the atomic IP spaces on compaet Lie groups.Also,we obtain the correspoding convergent rosults.展开更多
文摘In this paper,we use the representation of nilpotent Lie group method to give a sufficient and necessary condition for subellipticity of Left invarient differental operators on nilpotent Lipgroup G^2n+k.
文摘In this paer we will study the wellposed of the inital value problem associated to the homogeneous left invariant differential operator on the Heisenberg group by the method of group Forier anasis L=(-1)^k/2^k ∑j=1^1 aj(Zj^k Zj^-k+Zj^-kZj^k)+(-i)^3k rS^k(where aj>0,r∈R)on the Heisenboerg group,then obtain the explicit expression of the fundamental solutions for the generalized heat operator δ/δt+L and the operator L.
文摘The left invariant differential operators on a nilpotent Lie group which is elliptic on the generating direction have been widely studied, but little has been performed on the other kinds of differential operators [8]. UP to now, no example which is nonhomogenerous differential operators is available. In this paper. One left invariant differential operator not of transitive elliptic type is studied, and one of its fundamental solutions is given by the method of representations of nilpotent Lie groups.
文摘In this paper we discuss the weak type(IP,I)boundedness of a class of maximal operators T and themaximal strong,mean boundedness of a family of the operators {T on the atomic IP spaces on compaet Lie groups.Also,we obtain the correspoding convergent rosults.
