Applying the decomposition theorems in [1] and [2] , we obtain the boundedness theorem of Calderbn-Zygmund operator of type 6 on the Hardy spaces of weighted Herz type and establish interpolation theorem of linear ope...Applying the decomposition theorems in [1] and [2] , we obtain the boundedness theorem of Calderbn-Zygmund operator of type 6 on the Hardy spaces of weighted Herz type and establish interpolation theorem of linear operators on the weighted Herz spaces. -展开更多
In this paper, the complete convergence for the weighted sums of independent and identically distributed random variables in Stout [9] is improved and extended under NOD setup.The more optimal moment condition is give...In this paper, the complete convergence for the weighted sums of independent and identically distributed random variables in Stout [9] is improved and extended under NOD setup.The more optimal moment condition is given. The main results also hold for END sequence.展开更多
In this paper, we study the weighted (0,2;0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤3n-1 when the function values are prescribed at two sets of points namely the zeros of...In this paper, we study the weighted (0,2;0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤3n-1 when the function values are prescribed at two sets of points namely the zeros of H n(x) and H ′ n(x) and the wieghted second derivative at the zeros of H n(x).展开更多
In this paper we obtain the fundamental solution for a class of weighted BaouendiGrushin type operator L_(p,γ,α)u = ▽_γ·(|▽_γu|^(p-2)ρ~α▽_γu) on R^(m+n )with singularity at the origin,where ▽_γ is the...In this paper we obtain the fundamental solution for a class of weighted BaouendiGrushin type operator L_(p,γ,α)u = ▽_γ·(|▽_γu|^(p-2)ρ~α▽_γu) on R^(m+n )with singularity at the origin,where ▽_γ is the gradient operator defined by ▽_γ =(▽_x,|x|~γ▽_y) and ρ is the distance function.As an application,we get some Hardy type inequalities associated with ▽_γ.展开更多
Let K be the Calderón-Zygmund convolution kernel on R^d(d≥2).Christ and Journé defined the commutator associated with K and a∈L~∞(R^d)by T_af(x)=p.v.∫_(R^d)K(x-y)m_x,y^a·f(y)dy,which is an extension...Let K be the Calderón-Zygmund convolution kernel on R^d(d≥2).Christ and Journé defined the commutator associated with K and a∈L~∞(R^d)by T_af(x)=p.v.∫_(R^d)K(x-y)m_x,y^a·f(y)dy,which is an extension of the classical Calderón commutator. In this paper, we show that T_a is weighted weak type(1,1) bounded with A,1 weight for d≥2.展开更多
Let p>0 andνbe a normal function on[0,1).In this paper,several equivalent characterizations are given for which composition operators are bounded or compact on the normal weight Dirichlet type space D_(ν)^(p)(D)i...Let p>0 andνbe a normal function on[0,1).In this paper,several equivalent characterizations are given for which composition operators are bounded or compact on the normal weight Dirichlet type space D_(ν)^(p)(D)in the unit disc.展开更多
We show the existence and multiplicity of solutions to degenerate p(x)-Laplace equations with Leray-Lions type operators using direct methods and critical point theories in Calculus of Variations and prove the uniquen...We show the existence and multiplicity of solutions to degenerate p(x)-Laplace equations with Leray-Lions type operators using direct methods and critical point theories in Calculus of Variations and prove the uniqueness and nonnegativeness of solutions when the principal operator is monotone and the nonlinearity is nonincreasing. Our operator is of the most general form containing all previous ones and we also weaken assumptions on the operator and the nonlinearity to get the above results. Moreover, we do not impose the restricted condition on p(x) and the uniform monotonicity of the operator to show the existence of three distinct solutions.展开更多
基金Supported by NSF of China and the Fund of Doctoral Program of N.E.C.
文摘Applying the decomposition theorems in [1] and [2] , we obtain the boundedness theorem of Calderbn-Zygmund operator of type 6 on the Hardy spaces of weighted Herz type and establish interpolation theorem of linear operators on the weighted Herz spaces. -
基金Supported by the National Natural Science Foundation of China(11271161)
文摘In this paper, the complete convergence for the weighted sums of independent and identically distributed random variables in Stout [9] is improved and extended under NOD setup.The more optimal moment condition is given. The main results also hold for END sequence.
文摘In this paper, we study the weighted (0,2;0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤3n-1 when the function values are prescribed at two sets of points namely the zeros of H n(x) and H ′ n(x) and the wieghted second derivative at the zeros of H n(x).
基金Foundation item： Supported by the Natural Science Foundation of Zhejiang Province（Y6090359, Y6090383） Supported by the Department of Education of Zhejiang Province（Z200803357）
文摘In this paper we obtain the fundamental solution for a class of weighted BaouendiGrushin type operator L_(p,γ,α)u = ▽_γ·(|▽_γu|^(p-2)ρ~α▽_γu) on R^(m+n )with singularity at the origin,where ▽_γ is the gradient operator defined by ▽_γ =(▽_x,|x|~γ▽_y) and ρ is the distance function.As an application,we get some Hardy type inequalities associated with ▽_γ.
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)the Fundamental Research Funds for the Central Universities (Grant No. 2014KJJCA10)
文摘Let K be the Calderón-Zygmund convolution kernel on R^d(d≥2).Christ and Journé defined the commutator associated with K and a∈L~∞(R^d)by T_af(x)=p.v.∫_(R^d)K(x-y)m_x,y^a·f(y)dy,which is an extension of the classical Calderón commutator. In this paper, we show that T_a is weighted weak type(1,1) bounded with A,1 weight for d≥2.
基金supported by the National Natural Science Foundation of China(Grant No.11942109).
文摘Let p>0 andνbe a normal function on[0,1).In this paper,several equivalent characterizations are given for which composition operators are bounded or compact on the normal weight Dirichlet type space D_(ν)^(p)(D)in the unit disc.
基金supported by the National Research Foundation of Korea Grant Funded by the Korea Government (Grant No. NRF-2015R1D1A3A01019789)
文摘We show the existence and multiplicity of solutions to degenerate p(x)-Laplace equations with Leray-Lions type operators using direct methods and critical point theories in Calculus of Variations and prove the uniqueness and nonnegativeness of solutions when the principal operator is monotone and the nonlinearity is nonincreasing. Our operator is of the most general form containing all previous ones and we also weaken assumptions on the operator and the nonlinearity to get the above results. Moreover, we do not impose the restricted condition on p(x) and the uniform monotonicity of the operator to show the existence of three distinct solutions.
