In this paper,we focus on studying weighted Poincare inequalities on stratified Lie groups.We derive various Poincaréinequalities in the case 1<p=q<∞ in the high order Sobolev space Wm,p.We derive several ...In this paper,we focus on studying weighted Poincare inequalities on stratified Lie groups.We derive various Poincaréinequalities in the case 1<p=q<∞ in the high order Sobolev space Wm,p.We derive several Poincare inequalities that complement existing results,which have only been proved for the case 1<p<q<∞.展开更多
In this paper we prove that the Jacobian J（F） of a map F（f1,…,f1 from Ginto Rt maps the product of Lebesgue space Lp1×…× Lp1 into local Hardy space hY（G）,whereQ/Q＋1〈r〈1,and Q is the homogeneous dim...In this paper we prove that the Jacobian J（F） of a map F（f1,…,f1 from Ginto Rt maps the product of Lebesgue space Lp1×…× Lp1 into local Hardy space hY（G）,whereQ/Q＋1〈r〈1,and Q is the homogeneous dimension of the stratified Lie group G.展开更多
Let G be a stratified Lie group and let{X_(1)……,X_(n1)}be a basis of the first layer of the Lie algebra of G.The sub-Laplacian△G is defined by△G=-n_(1)∑j=1 X^(2)j,The operator defined by△G-n_(1)∑j=1 Xjp/pXj is ...Let G be a stratified Lie group and let{X_(1)……,X_(n1)}be a basis of the first layer of the Lie algebra of G.The sub-Laplacian△G is defined by△G=-n_(1)∑j=1 X^(2)j,The operator defined by△G-n_(1)∑j=1 Xjp/pXj is called the Ornstein-Uhlenbeck operator on G,where p is a heat kernel at time 1 on G.In this paper,we investigate Gaussian BV functions and Gaussian BV capacities associated with the Ornstein-Uhlenbeck operator on the stratified Lie group.展开更多
Abstract. Let H^n be the Heisenberg group and Q = 2n＋2 be its homogeneous dimen- sion. In this paper, we consider the Schr6dinger operator -△H^n ＋V, where △H^n is the sub-Laplacian and V is the nonnegative potenti...Abstract. Let H^n be the Heisenberg group and Q = 2n＋2 be its homogeneous dimen- sion. In this paper, we consider the Schr6dinger operator -△H^n ＋V, where △H^n is the sub-Laplacian and V is the nonnegative potential belonging to the reverse H61der class Bql for ql _〉 Q/2. We show that the operators T1 = V（-△H^n-In ＋V）-1 and T2 = V1/2（-△H^n-V）-1/2 are both bounded from 1 n HL^1（H^n ） into L1（H^n）. Our results are also valid on the stratified Lie group.展开更多
Let X be an RD-space. In this paper, the authors establish the boundedness of the commutator Tbf = bTf-T(bf) on Lp , p∈(1,∞), where T is a Calderón-Zygmund operator related to the admissible function ρ and b∈...Let X be an RD-space. In this paper, the authors establish the boundedness of the commutator Tbf = bTf-T(bf) on Lp , p∈(1,∞), where T is a Calderón-Zygmund operator related to the admissible function ρ and b∈BMOθ(X)BMO(X). Moreover, they prove that Tb is bounded from the Hardy space H1ρ(X) into the weak Lebesgue space L1weak(X). This can be used to deal with the Schrdinger operators and Schrdinger type operators on the Euclidean space Rn and the sub-Laplace Schrdinger operators on the stratified Lie group G.展开更多
文摘In this paper,we focus on studying weighted Poincare inequalities on stratified Lie groups.We derive various Poincaréinequalities in the case 1<p=q<∞ in the high order Sobolev space Wm,p.We derive several Poincare inequalities that complement existing results,which have only been proved for the case 1<p<q<∞.
文摘In this paper we prove that the Jacobian J（F） of a map F（f1,…,f1 from Ginto Rt maps the product of Lebesgue space Lp1×…× Lp1 into local Hardy space hY（G）,whereQ/Q＋1〈r〈1,and Q is the homogeneous dimension of the stratified Lie group G.
基金supported by Fundamental Research Funds for the Central Universities(No.500421126)Pengtao Li was in part supported by Shandong Natural Science Foundation of China(No.ZR2017JL008)+2 种基金National Natural Science Foundation of China(Nos.11871293 and 12071272)Yu Liu was supported by National Natural Science Foundation of China(No.11671031)Beijing Municipal Science and Technology Project(No.Z17111000220000).
文摘Let G be a stratified Lie group and let{X_(1)……,X_(n1)}be a basis of the first layer of the Lie algebra of G.The sub-Laplacian△G is defined by△G=-n_(1)∑j=1 X^(2)j,The operator defined by△G-n_(1)∑j=1 Xjp/pXj is called the Ornstein-Uhlenbeck operator on G,where p is a heat kernel at time 1 on G.In this paper,we investigate Gaussian BV functions and Gaussian BV capacities associated with the Ornstein-Uhlenbeck operator on the stratified Lie group.
文摘Abstract. Let H^n be the Heisenberg group and Q = 2n＋2 be its homogeneous dimen- sion. In this paper, we consider the Schr6dinger operator -△H^n ＋V, where △H^n is the sub-Laplacian and V is the nonnegative potential belonging to the reverse H61der class Bql for ql _〉 Q/2. We show that the operators T1 = V（-△H^n-In ＋V）-1 and T2 = V1/2（-△H^n-V）-1/2 are both bounded from 1 n HL^1（H^n ） into L1（H^n）. Our results are also valid on the stratified Lie group.
基金National Natural Science Foundation of China (Grant Nos. 10901018 and 11001002)the Shanghai Leading Academic Discipline Project (Grant No. J50101)the Fundamental Research Funds for the Central Universities
文摘Let X be an RD-space. In this paper, the authors establish the boundedness of the commutator Tbf = bTf-T(bf) on Lp , p∈(1,∞), where T is a Calderón-Zygmund operator related to the admissible function ρ and b∈BMOθ(X)BMO(X). Moreover, they prove that Tb is bounded from the Hardy space H1ρ(X) into the weak Lebesgue space L1weak(X). This can be used to deal with the Schrdinger operators and Schrdinger type operators on the Euclidean space Rn and the sub-Laplace Schrdinger operators on the stratified Lie group G.
