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| 1 | THE CENTRAL BMO SPACES AND LITTLEWOOD-PALEY OPERATORS显示文摘The authors give a characterization of central bounded mean oscillation space CBMO2(Rγ) in terms of the central Carleson measure. Using this character, the authors establish the CBMO2(Rγ)-boundedness for several classes of general Littlewood-Paley operators. | Lu Shanzhen and Yang Dachun (Beijing Normal University, China) | 1995 | Analysis in Theory and Applications1995，11，3： | 49 |
| 2 | BIVARIATE BLENDING RATIONAL INTERPOLANTS显示文摘Bath the Newton inter polating polynomials and the Thiele-type inter polating continued fractions based on inverse differences are used to construct a kind of blending rational inter polants and an error estimation is grven. | Tan Jieqing(Hefei University of Technology, China) | 1999 | Analysis in Theory and Applications1999，15，2： | 30 |
| 3 | UNIQUE COMMON FIXED POINT OF A FAMILY OF SELF-MAPS WITH SAME TYPE CONTRACTIVE CONDITION IN 2-METRIC SPACE显示文摘In this paper, we prove that a family of self-maps {Ti,j}i,j∈N in 2-metric space has a unique common fixed point if (i) {Ti,j}i,j∈N satisfies the same type contractive condition for each j ∈ N; (ii) Tm,μ· Tn,ν = Tn,ν· Tm,μ for all m,n,μ,ν∈ N with μ = ν. Our main result generalizes and improves many known unique common fixed point theorems in 2-metric spaces. | Yongjie Piao | 2008 | Analysis in Theory and Applications2008，24，4： | 15 |
| 4 | ON THE DEGREE OF APPROXIMATION BY WAVELET EXPANSIONS显示文摘In this paper we estimate the degree of approximation of wavelet expansions. Our result shows that the degree has the exponential decay for function f(x) ∈ L2 continuous in a finite interval (a,b) which is much superior to those of approximation by polynomial operators and by expansions of classical orthogonal series. | Sun Xiehua (China Institute of Metrology, China) | 1998 | Analysis in Theory and Applications1998，14，1： | 15 |
| 5 | THE CURL IN SEVEN DIMENSIONAL SPACE AND ITS APPLICATIONS显示文摘In higher dimensional spaces Rn(n>3) the usual curl does not have the properties as in R3. In this paper, we established the natural concept of curl in R7 via octonion O. We prove that there exists the curl in Rn if and only if n=3, 7. Some applications are presented, such as the new phenmenon of the differential forms in R7 whcih is different from the ordinary de Rham cohomology and Hodge theory, grad-curl-div type Dirac oper ator in R6, seven dimensional Maxwell equations and Navier-Stokes equations.Supported by the National Natural Science Foundation Of | Lizhong Peng (1) Lei Yang (1) | 1999 | Analysis in Theory and Applications1999，15，3： | 12 |
| 6 | ON STEIN-WEISS CONJUGATE HARMONIC FUNCTION AND OCTONION ANALYTIC FUNCTION显示文摘It is shown that the Stein-Weiss conjugate harmaonic funciton is the Octonion analytic function. We find a counter example to show the converse is not ture in the Octonion case, by which wehave answered the question proposed in [1]. | Li Xingmin Peng Lizhong | 2000 | Analysis in Theory and Applications2000，16，2： | 11 |
| 7 | BIFURCATION ANALYSIS AND FEEDBACK CONTROL OF A 3D CHAOTIC SYSTEM显示文摘In this paper,we analyze a three-dimensional differential system derived from the Chen system based on the first Lyapunov coefficient,and apply it to investigate the local bifurcation.And we present some insights on bifurcation and stability,also obtain some conditions for subcritical and supercritical.Finally,we give some numerical simulation studies of system in order to verify analytic results. | Zhen Wang | 2007 | Analysis in Theory and Applications2007，23，4： | 11 |
| 8 | BOUNDEDNESS OF VECTOR-VALUED OPERATORS ON WEIGHTED HERZ SPACES显示文摘In this paper, the authors establish the weighted weak and strong type norm inequalities in the set of weighted Herz-type spaces for a vector-valued analogue o f the Hardy-Littlewood maximal operator; and using this,the authors obtain the weighted inequalies for a wide class of sublinear singular operators defined on Rn which include the Calderon-Zygmund operators as special cases. The fractional versions of these results are also given. | Tang Lin Yang Dachun | 2000 | Analysis in Theory and Applications2000，16，2： | 11 |
| 9 | DEGREE OF APPROXIMATION BY SUPERPOSITIONS OF A SIGMOIDAL FUNCTION显示文摘In this paper we study the degree of approximation by superpositions of a sigmoidal function.We mainlyconsider the univariate case.If f is a continuous function,we prove that for any bounded sigmoidalfunction σ,dn,σ(f)≤‖σ‖ω(f,1/(n+1)).For the Heaviside function H(x),we prove that dn,H(f)≤ω(f,1/(2(n+1))).If f is a continuous funnction of bounded variation,we prove that dn,σ(f)≤‖σ‖/(n+1)V(f)and dn,H(f)≤1/(2(n+1))V(f).For he Heaviside function,the coefficient 1 and the approximation orders are the bestpossible.We compare these results with the classical Jackson and Bernstein theorems,and make some conjec-tures for further study. | Chen Debao (University of Texas at Austin,USA) | 1993 | Analysis in Theory and Applications1993，9，3： | 11 |
| 10 | ON NEWMAN-TYPE RATIONAL INTERPOLATION TO |x| AT THE CHEBYSHEV NODES OF THE SECOND KIND显示文摘最近, Brutman 和 Passow 认为 Newman 类型合理插值是 to|x |由对称的节点的任意的集合导致了在[-1,1] 并且给了近似错误的一般评价。由他们的方法,一个人能为一些特殊节点建立近似的准确顺序。在我们考虑插值节点是第二种类型的零个 Chebyshev 多项式并且在这种情况中证明那的特殊情况的现在的纸,近似的准确顺序是 O (1/(n ln n )) 。 | Laiyi Zhu Zhaolin Dong | 2006 | Analysis in Theory and Applications2006，22，3： | 10 |
| 11 | ON N-WIDTHS OF SOME PERIODIC CONVOLUTION CLASSES IN ORLICZ SPACES显示文摘In this paper we extend the some accurate results on n-width of Sobolevclass W_∞~γ in L_p spaces to Orlicz spaces,and establish the correspondingresults for dual cases. | Wu Garidi (Inner Mongolia Normal University,China) | 1998 | Analysis in Theory and Applications1998，14，3： | 10 |
| 12 | SHIFT-INVARIANT BI-INNER PRODUCT FUNCTIONALS ARE INNER PRODUCTS显示文摘Bi-inner product functionals generated by a pair of Bessel sequences of L2 functions are introduced. It is shown that these functionals are constant multiples of the inner products of L2 and l2, if and only if they are shift-invariant both in space (or time) and in Phase. This result is then applied to characterize dual frames and bi-orthogonal Riesz bases of | Charles K. Chui (1) Xianliang Shi (1) | 1999 | Analysis in Theory and Applications1999，15，1： | 10 |
| 13 | THE HAUSDORFF MEASURE OF GENERALIZED SIERPINSKI CARPETS显示文摘Let 0 | Zhu Yucan Lou Jun | 2000 | Analysis in Theory and Applications2000，16，2： | 9 |
| 14 | On the Relation of Shadowing and Expansivity in Nonautonomous Discrete Systems显示文摘In this paper we study shadowing property for sequences of mappings on compact metric spaces,i.e.,nonautonomous discrete dynamical systems.We investigate the relations of various expansivity properties with shadowing and h-shadowing property. | Hossein Rasuli Reza Memarbashi | 2017 | Analysis in Theory and Applications2017，33，1： | 8 |
| 15 | ON LAGRANGE INTERPOLATION TO |x|α(1 < α < 2) WITH EQUALLY SPACED NODES显示文摘S.M. Lozinskii proved the exact convergence rate at the zero of Lagrange interpolation polynomials to |x| based on equidistant nodes in [-1, 1]. In 2000, M. Rever generalized S.M. Lozinskii's result to |x|α(0 ≤α≤ 1). In this paper we will present the exact rate of convergence at the point zero for the interpolants of |x|α(1 <α< 2).. | XiaMao | 2004 | Analysis in Theory and Applications2004，20，3： | 8 |
| 16 | DEGREE OF APPROXIMATION ASSOCIATED WITH SOME ELLIPTIC OPERATORS AND ITS APPLICATIONS显示文摘The Jackson-type estimates by using some elliptic operators will be achieved. These results will be used to characterize the regularity of some elliptic operators by means of the approximation degree and the saturation class of the multivariate Bernstein operators as well. | Xinlong Zhou(University of Duisburg, Germany) | 1995 | Analysis in Theory and Applications1995，11，2： | 8 |
| 17 | CONNECTION BETWEEN THE ORDER OF FRACTIONAL CALCULUS AND FRACTIONAL DIMENSIONS OF A TYPE OF FRACTAL FUNCTIONS显示文摘The linear relationship between fractal dimensions of a type of generalized Weierstrass functions and the order of their fractional calculus has been proved.The graphs and numerical results given here further indicate the corresponding relationship. | Yongshun Liang Weiyi Su | 2007 | Analysis in Theory and Applications2007，23，4： | 7 |
| 18 | A FAMILY OF BERNSTEIN QUASI-INTERPOLANTS ON[0,1]显示文摘Suppose that we want to approximate fC[0,1]by polynomials in Pn,using only itsvalues on Xn={i/n,0≤i≤n}.This can be done by the Lagrange interpolant Ln f or theclassical Bernstein polynomial Bn f.But,when n tends to infinity,Ln f does not converge to fin general and the convergence of Bn f to fis very slow.We define a family of operators Bkn,n≥k,which are intermediate ones between B(0)n=B1n=Bn and Bnn=Ln,and we studysome of their properties.In particular,we prove a Voronovskaja-type theorem which assertsthat Bkn f-f=0(n-[(k+2)/2)for f sufficiently regular.Moreover,B(k)n f uses only values of Bn f and its derivaties and can be computed by DeCasteljau or subdivision algorithms. | P.Sablonniere | 1992 | Analysis in Theory and Applications1992，8，3： | 7 |
| 19 | A NOTE ON MODIFIED BASKAKOV TYPE OPERATORS显示文摘In the present paper, we define a new kind of positive linear operators and study the rate ofconvergence in simultaneous approximation. This operator being capable of providing better approxima-tion than modified Baskakov operators. | Vijay Gupta | 1994 | Analysis in Theory and Applications1994，10，3： | 7 |
| 20 | INHOMOGENEOUS BESOV AND TRIEBEL-LIZORKING SPACES ON SPACES OF HOMOGENEOUS TYPE显示文摘The authors introduce the inhomogeneous esov space and the inhomogeneous Triebel-Lizorkin space on spaces of homogeneous type; and present their atom and molecule decompositions, their dual spaces and the complex interpolation theorems. They also establishe the relation between the homogoeneous Besov space and the inhomogeneous one, and between the homogeneous Triebel-Lizorkin space and the inhomogeneous one. Moreover,they establish T1 theorems for these inhomogeneous spaces when a≠0, and applythese T1 theorems to give new characterizations of these | Yongsheng Han (1) Shanzhen Lu (2) Dachun Yang (2) | 1999 | Analysis in Theory and Applications1999，15，3： | 6 |
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