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
In this paper, we study a kind of oscillatory singular integral operator T with Calderon-Zygmund kernel, which had been studied by Ricci and Stein in [6], and extend their result. We get that T is bounded on L^P（R^...In this paper, we study a kind of oscillatory singular integral operator T with Calderon-Zygmund kernel, which had been studied by Ricci and Stein in [6], and extend their result. We get that T is bounded on L^P（R^n）（1〈p〈∞） when -1〈u〈 αd（1/2-｜1/p-1/2）.展开更多
In this paper,we use the method of representation of Lie group to study a class of nonhomoge- neous convolution operator on the nilpotent Lie group H^M×R^k,and give a criteerion of their hypoellipticity.
In this paper, we consider a class of singularly perturbed Dirichlet exterior problems for elliptic equations. Under the appropriate conditions we construct the formally asymptotic solution of the problem described. U...In this paper, we consider a class of singularly perturbed Dirichlet exterior problems for elliptic equations. Under the appropriate conditions we construct the formally asymptotic solution of the problem described. Using differential inequaltiy theory we prove the existence of the solution of original problem and the uniforly validity of the formal solution.展开更多
In this paper the authors study proprieties of certain convolution operators on L (G) and weighted BMO(a)(G) spaces,where G is a locally compact totally disconnected group with a suitable sequence of open compact sub...In this paper the authors study proprieties of certain convolution operators on L (G) and weighted BMO(a)(G) spaces,where G is a locally compact totally disconnected group with a suitable sequence of open compact subgroups. The authors prove that if the kernel satisfies certain conditions, then the convolution operator is bounded from L to BMO(a) or from BMO(a) to BMO().展开更多
Let A :=(A_1, A_2) be a pair of expansive dilations and φ : R^n×R^m×[0, ∞) → [0, ∞) an anisotropic product Musielak-Orlicz function. In this article, we introduce the anisotropic product Musielak-Orlicz ...Let A :=(A_1, A_2) be a pair of expansive dilations and φ : R^n×R^m×[0, ∞) → [0, ∞) an anisotropic product Musielak-Orlicz function. In this article, we introduce the anisotropic product Musielak-Orlicz Hardy space H~φ_A(R^n× R^m) via the anisotropic Lusin-area function and establish its atomic characterization, the g-function characterization, the g_λ~*-function characterization and the discrete wavelet characterization via first giving out an anisotropic product Peetre inequality of Musielak-Orlicz type. Moreover, we prove that finite atomic decomposition norm on a dense subspace of H~φ_A(R^n× R^m) is equivalent to the standard infinite atomic decomposition norm. As an application, we show that, for a given admissible triplet(φ, q, s), if T is a sublinear operator and maps all(φ, q, s)-atoms into uniformly bounded elements of some quasi-Banach spaces B, then T uniquely extends to a bounded sublinear operator from H~φ_A(R^n× R^m) to B. Another application is that we obtain the boundedness of anisotropic product singular integral operators from H~φ_A(R^n× R^m) to L~φ(R^n× R^m)and from H~φ_A(R^n×R^m) to itself, whose kernels are adapted to the action of A. The results of this article essentially extend the existing results for weighted product Hardy spaces on R^n× R^m and are new even for classical product Orlicz-Hardy spaces.展开更多
LP mapping properties are considered for a class of oscillatory signular integral operators.Ketwords:Calderon-Zygmund kernel. oscillatory singular integral operator. polynomial growth estimate.
We consider the boundedness of the rough singular integral operator T_（？,ψ,h） along a surface of revolution on the Triebel-Lizorkin space F^α_（ p,q）（R^n） for Ω ∈ H^1（（S^n-1）） and Ω ∈ Llog^＋L（S^n-1）...We consider the boundedness of the rough singular integral operator T_（？,ψ,h） along a surface of revolution on the Triebel-Lizorkin space F^α_（ p,q）（R^n） for Ω ∈ H^1（（S^n-1）） and Ω ∈ Llog^＋L（S^n-1） ∪_1展开更多
In this paper, by sharp function estimates and certain weak type endpoint estimates, the authors establish some weighted norm inequalities with Ap weights for the multilinear singular integral operators with non-smoot...In this paper, by sharp function estimates and certain weak type endpoint estimates, the authors establish some weighted norm inequalities with Ap weights for the multilinear singular integral operators with non-smooth kernels.展开更多
Let TΩ be the singular integral operator with kernel Ω（x）/｜x｜n where is homogeneous of degree zero, integrable and has mean value zero on the unit sphere Sn-1. In this paper, by Fourier transform estimates, L...Let TΩ be the singular integral operator with kernel Ω（x）/｜x｜n where is homogeneous of degree zero, integrable and has mean value zero on the unit sphere Sn-1. In this paper, by Fourier transform estimates, Littlewood-Paley theory and approximation, the authors prove that if Ω∈（lnL）2 （Sn- 1）, then the commutator generated by TΩ and CMO（Rn） function, and the corresponding discrete maximal operator, are compact on LP（Rn, ｜s｜γp） for p∈ （1, ∞） and γp ∈ （-1, p-l）展开更多
We study the maximal super-singular integral operator T＊Ω,α,β（f）（x,y）=sup ∈1〉0,∈2〉0｜∫｜u｜〉ε1,｜v｜〉ε2 b1（｜u｜）b2（｜u｜）Ω（u＇,u＇）/｜u｜^n＋α｜u｜^m＋β-f（x-u,y-u）dudu｜defined on all f ...We study the maximal super-singular integral operator T＊Ω,α,β（f）（x,y）=sup ∈1〉0,∈2〉0｜∫｜u｜〉ε1,｜v｜〉ε2 b1（｜u｜）b2（｜u｜）Ω（u＇,u＇）/｜u｜^n＋α｜u｜^m＋β-f（x-u,y-u）dudu｜defined on all f ∈ S（R^n ×R^m）, where 0 ≤ α,β〈∞, b1 b2 ∈ L∞（R＋1 ）,Ω satisfies certain cancellation conditions and Ω∈L1（S^n-1×S^m-1）in the case α,β〉0;Ω∈L（log＋L）（S^n-1×S^m-1）in the case αβ=0 and α＋β 〉0. It is proved that, for 1〈p〈∞.T＊Ω,α,βis a bounded operator from the homogeneous Sobolev space Lα,β^p（R^n×R^m）to the Lebesgue space L^p（R^n×R^m）.展开更多
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In this paper, we study a kind of oscillatory singular integral operator T with Calderon-Zygmund kernel, which had been studied by Ricci and Stein in [6], and extend their result. We get that T is bounded on L^P（R^n）（1〈p〈∞） when -1〈u〈 αd（1/2-｜1/p-1/2）.
文摘In this paper,we use the method of representation of Lie group to study a class of nonhomoge- neous convolution operator on the nilpotent Lie group H^M×R^k,and give a criteerion of their hypoellipticity.
文摘In this paper, we consider a class of singularly perturbed Dirichlet exterior problems for elliptic equations. Under the appropriate conditions we construct the formally asymptotic solution of the problem described. Using differential inequaltiy theory we prove the existence of the solution of original problem and the uniforly validity of the formal solution.
文摘In this paper the authors study proprieties of certain convolution operators on L (G) and weighted BMO(a)(G) spaces,where G is a locally compact totally disconnected group with a suitable sequence of open compact subgroups. The authors prove that if the kernel satisfies certain conditions, then the convolution operator is bounded from L to BMO(a) or from BMO(a) to BMO().
基金supported by National Natural Science Foundation of China (Grant Nos. 11671414, 11271091, 11471040, 11461065, 11661075, 11571039 and 11671185)
文摘Let A :=(A_1, A_2) be a pair of expansive dilations and φ : R^n×R^m×[0, ∞) → [0, ∞) an anisotropic product Musielak-Orlicz function. In this article, we introduce the anisotropic product Musielak-Orlicz Hardy space H~φ_A(R^n× R^m) via the anisotropic Lusin-area function and establish its atomic characterization, the g-function characterization, the g_λ~*-function characterization and the discrete wavelet characterization via first giving out an anisotropic product Peetre inequality of Musielak-Orlicz type. Moreover, we prove that finite atomic decomposition norm on a dense subspace of H~φ_A(R^n× R^m) is equivalent to the standard infinite atomic decomposition norm. As an application, we show that, for a given admissible triplet(φ, q, s), if T is a sublinear operator and maps all(φ, q, s)-atoms into uniformly bounded elements of some quasi-Banach spaces B, then T uniquely extends to a bounded sublinear operator from H~φ_A(R^n× R^m) to B. Another application is that we obtain the boundedness of anisotropic product singular integral operators from H~φ_A(R^n× R^m) to L~φ(R^n× R^m)and from H~φ_A(R^n×R^m) to itself, whose kernels are adapted to the action of A. The results of this article essentially extend the existing results for weighted product Hardy spaces on R^n× R^m and are new even for classical product Orlicz-Hardy spaces.
文摘LP mapping properties are considered for a class of oscillatory signular integral operators.Ketwords:Calderon-Zygmund kernel. oscillatory singular integral operator. polynomial growth estimate.
基金supported by National Natural Science Foundation of China (Grant Nos. 11371057, 11471033 and 11571160)Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20130003110003)+2 种基金the Fundamental Research Funds for the Central Universities (Grant No. 2014KJJCA10)Grant-in-Aid for Scientific Research (C) (Grant No. 23540228)Japan Society for the Promotion of Science
文摘We consider the boundedness of the rough singular integral operator T_（？,ψ,h） along a surface of revolution on the Triebel-Lizorkin space F^α_（ p,q）（R^n） for Ω ∈ H^1（（S^n-1）） and Ω ∈ Llog^＋L（S^n-1） ∪_1
基金supported by National Natural Science Foundation of China (Grant No. 10971228),supported by National Natural Science Foundation of China (Grant Nos. 10871024, 10931001)
文摘In this paper, by sharp function estimates and certain weak type endpoint estimates, the authors establish some weighted norm inequalities with Ap weights for the multilinear singular integral operators with non-smooth kernels.
基金supported by National Natural Science Foundation of China(Grant No.11371370)
文摘Let TΩ be the singular integral operator with kernel Ω（x）/｜x｜n where is homogeneous of degree zero, integrable and has mean value zero on the unit sphere Sn-1. In this paper, by Fourier transform estimates, Littlewood-Paley theory and approximation, the authors prove that if Ω∈（lnL）2 （Sn- 1）, then the commutator generated by TΩ and CMO（Rn） function, and the corresponding discrete maximal operator, are compact on LP（Rn, ｜s｜γp） for p∈ （1, ∞） and γp ∈ （-1, p-l）
基金supported by National Natural Science Foundation of China (Grant Nos. 10871173, 10931001)
文摘We study the maximal super-singular integral operator T＊Ω,α,β（f）（x,y）=sup ∈1〉0,∈2〉0｜∫｜u｜〉ε1,｜v｜〉ε2 b1（｜u｜）b2（｜u｜）Ω（u＇,u＇）/｜u｜^n＋α｜u｜^m＋β-f（x-u,y-u）dudu｜defined on all f ∈ S（R^n ×R^m）, where 0 ≤ α,β〈∞, b1 b2 ∈ L∞（R＋1 ）,Ω satisfies certain cancellation conditions and Ω∈L1（S^n-1×S^m-1）in the case α,β〉0;Ω∈L（log＋L）（S^n-1×S^m-1）in the case αβ=0 and α＋β 〉0. It is proved that, for 1〈p〈∞.T＊Ω,α,βis a bounded operator from the homogeneous Sobolev space Lα,β^p（R^n×R^m）to the Lebesgue space L^p（R^n×R^m）.
