Let G be an Abelian group and letρ：G×G→[0,∞） be a metric on G. Let E be a normed space. We prove that under some conditions if f：G→E is an odd function and Cx：G→E defined by Cx（y）：=2 f （x＋y）＋2 f ...Let G be an Abelian group and letρ：G×G→[0,∞） be a metric on G. Let E be a normed space. We prove that under some conditions if f：G→E is an odd function and Cx：G→E defined by Cx（y）：=2 f （x＋y）＋2 f （x-y）＋12 f （x）-f （2x＋y）-f （2x-y） is a cubic function for all x∈G, then there exists a cubic function C：G→E such that f？C is Lipschitz. Moreover, we investigate the stability of cubic functional equation 2 f （x＋y）＋2 f （x-y）＋12 f （x）-f （2x＋y）-f （2x-y）=0 on Lipschitz spaces.展开更多
In this article, we obtain the LP-boundedness of commutators of Lipschitz functions and singular integrals with non-smooth kernels on Euclidean spaces.
The Lipschitz class Lip(K, α) on a local field K is defined in [10], and an equivalent relationship between the Ho¨lder type space Cα(K)[9] and Lip(K,α) is given. In this note, we give a 'chain of function...The Lipschitz class Lip(K, α) on a local field K is defined in [10], and an equivalent relationship between the Ho¨lder type space Cα(K)[9] and Lip(K,α) is given. In this note, we give a 'chain of function spaces' over Euclidian space by defining higher order continuous modulus in R, and point out that there is no need of higher order continuous modulus for describing the chain of function spaces over local fields.展开更多
In this paper, we will use a method of sharp maximal function approach to show the boundedness of commutator [b,TR^δ] by Bochner-Riesz operators and the function b on weighted Morrey spaces L^p,k （ω） under appro...In this paper, we will use a method of sharp maximal function approach to show the boundedness of commutator [b,TR^δ] by Bochner-Riesz operators and the function b on weighted Morrey spaces L^p,k （ω） under appropriate conditions on the weight w, where b belongs to Lipschitz space or weighted Lipschitz space.展开更多
In 2000, Kostyrko, Salat, and Wilczynski introduced and studied the concept of I-convergence of sequences in metric spaces where I is an ideal. The concept of I-convergence has a wide application in the field of Numbe...In 2000, Kostyrko, Salat, and Wilczynski introduced and studied the concept of I-convergence of sequences in metric spaces where I is an ideal. The concept of I-convergence has a wide application in the field of Number Theory, trigonometric series, summability theory, probability theory, optimization and approximation theory. In this article we introduce the double sequence spaces and ,for a modulus function f and study some of the properties of these spaces.展开更多
Let L be the infinitesimal generator of an analytic semigroup on L 2 (Rn)with Gaussian kernel bounds,and L-α/ 2 be the fractional integrals generated by L for 0< α<n.Let Tj,1 be the singular integral with nons...Let L be the infinitesimal generator of an analytic semigroup on L 2 (Rn)with Gaussian kernel bounds,and L-α/ 2 be the fractional integrals generated by L for 0< α<n.Let Tj,1 be the singular integral with nonsmooth kernel related to L,or Tj,1=I, Tj,2,Tj,4 be the linear operators,which are bounded on Lp(Rn)for 1<p<∞,and Tj,3=±I(j=1,2,···,m),where I is the identity operator.For b∈L 1 loc (Rn),denote the Toeplitz-type operator byΘαbfmj=1(Tj,1MbIαTj,2 + Tj,3MbIαTj,4),where Mb is a multiplication ope...展开更多
文摘Let G be an Abelian group and letρ：G×G→[0,∞） be a metric on G. Let E be a normed space. We prove that under some conditions if f：G→E is an odd function and Cx：G→E defined by Cx（y）：=2 f （x＋y）＋2 f （x-y）＋12 f （x）-f （2x＋y）-f （2x-y） is a cubic function for all x∈G, then there exists a cubic function C：G→E such that f？C is Lipschitz. Moreover, we investigate the stability of cubic functional equation 2 f （x＋y）＋2 f （x-y）＋12 f （x）-f （2x＋y）-f （2x-y）=0 on Lipschitz spaces.
文摘In this article, we obtain the LP-boundedness of commutators of Lipschitz functions and singular integrals with non-smooth kernels on Euclidean spaces.
文摘The Lipschitz class Lip(K, α) on a local field K is defined in [10], and an equivalent relationship between the Ho¨lder type space Cα(K)[9] and Lip(K,α) is given. In this note, we give a 'chain of function spaces' over Euclidian space by defining higher order continuous modulus in R, and point out that there is no need of higher order continuous modulus for describing the chain of function spaces over local fields.
基金supported by NSFC (NO. 11201003)Education Committee of Anhui Province (NO. KJ2011A138 and NO. KJ2012A133)
文摘In this paper, we will use a method of sharp maximal function approach to show the boundedness of commutator [b,TR^δ] by Bochner-Riesz operators and the function b on weighted Morrey spaces L^p,k （ω） under appropriate conditions on the weight w, where b belongs to Lipschitz space or weighted Lipschitz space.
文摘In 2000, Kostyrko, Salat, and Wilczynski introduced and studied the concept of I-convergence of sequences in metric spaces where I is an ideal. The concept of I-convergence has a wide application in the field of Number Theory, trigonometric series, summability theory, probability theory, optimization and approximation theory. In this article we introduce the double sequence spaces and ,for a modulus function f and study some of the properties of these spaces.
基金Supported by the NNSF of China(10571014)SEDF of China(20040027001)
文摘Let L be the infinitesimal generator of an analytic semigroup on L 2 (Rn)with Gaussian kernel bounds,and L-α/ 2 be the fractional integrals generated by L for 0< α<n.Let Tj,1 be the singular integral with nonsmooth kernel related to L,or Tj,1=I, Tj,2,Tj,4 be the linear operators,which are bounded on Lp(Rn)for 1<p<∞,and Tj,3=±I(j=1,2,···,m),where I is the identity operator.For b∈L 1 loc (Rn),denote the Toeplitz-type operator byΘαbfmj=1(Tj,1MbIαTj,2 + Tj,3MbIαTj,4),where Mb is a multiplication ope...
基金Supported by NNSF of China(11401120)Foundation for Distinguished Young Teachers in Higher Education of Guangdong Province(YQ2015126)+1 种基金Foundation for Young Innovative Talents in Higher Education of Guangdong(2014KQNCX111)Innovation Program of Higher Education of Guangdong(2015KTSCX105)
