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The Interpolation of Operators between Weighted Hardy Spaces and Weighted L^p Spaces 被引量:1
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作者 王月山 王伟民 《Chinese Quarterly Journal of Mathematics》 CSCD 2001年第2期54-58,共5页
The paper is given the interpolation of operators between weighted Hardy spaces and weighted L p spaces when w∈A 1 by Calderon Zygmund decomposition.
关键词 Calderon Zygmund decomposition interpolation of operator weighted Hardy space w-(p q s) atom
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A GENERALIZATION OF BOYD’S INTERPOLATION THEOREM
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作者 Kwok-Pun HO 《Acta Mathematica Scientia》 SCIE CSCD 2021年第4期1263-1274,共12页
Boyd^interpolation theorem for quasilinear operators is generalized in this paper,which gives a generalization for both the Marcinkiewicz interpolation theorem and Boyd^interpolation theorem.By using this new interpol... Boyd^interpolation theorem for quasilinear operators is generalized in this paper,which gives a generalization for both the Marcinkiewicz interpolation theorem and Boyd^interpolation theorem.By using this new interpolation theorem,we study the spherical fractional maximal functions and the fractional maximal commutators on rearrangement-invariant quasi-Banach function spaces.In particular,we obtain the mapping properties of the spherical fractional maximal functions and the fractional maximal commutators on generalized Lorentz spaces. 展开更多
关键词 interpolation of operator quasilinear operator rearrangement-invariant function space spherical fractional maximal function fractional maximal commutator generalized Lorentz space
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The Approximation Properties of Certain Interpolation Operators of Entire Exponential Type (1)
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作者 刘九芬 田继善 《Chinese Quarterly Journal of Mathematics》 CSCD 1993年第2期32-39,共8页
In this paper, the authers introduce certain entire exponential type interpolation operatots and study the convergence problem of these operatots in c(R) or Lp(R) (1≤p<∞)
关键词 entire exponential type interpolation operators covergence property
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GLOBAL SMOOTHNESS PRESERVATION BY BIVARIATE INTERPOLATION OPERATORS
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作者 S.G. Gal J. Szabados 《Analysis in Theory and Applications》 2003年第3期193-208,共16页
Extending the results of [4] in the univariate case, in this paper we prove that the bivariate interpolation polynomials of Hermite-Fejér based on the Chebyshev nodes of the first kind, those of Lagrange based o... Extending the results of [4] in the univariate case, in this paper we prove that the bivariate interpolation polynomials of Hermite-Fejér based on the Chebyshev nodes of the first kind, those of Lagrange based on the Chebyshev nodes of second kind and ±1, and those of bivariate Shepard operators, have the property of partial preservation of global smoothness, with respect to various bivariate moduli of continuity. 展开更多
关键词 bivariate interpolation polynomials and operators bivariate moduli of continuity global smoothness preservation
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On Approximation by Two Kinds Modified Durrmeyer Rational Interpolation Operators in Lω^M Spaces
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作者 ZHANG Xu WU Ga-ridi 《Chinese Quarterly Journal of Mathematics》 2018年第1期73-78,共6页
This paper discusses the approximation problem of two kinds Durrmeyer rational interpolation operators in Orlicz spaces with weight functions,and gives a kind of Jackson type estimation of approximation order by means... This paper discusses the approximation problem of two kinds Durrmeyer rational interpolation operators in Orlicz spaces with weight functions,and gives a kind of Jackson type estimation of approximation order by means of continuous modulus, Hardy-Littlewood maximal function, convexity of N function and Jensen inequality. 展开更多
关键词 Weighted Orlicz spaces Rational interpolation type operator Jackson type estimation
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On the Method of Multiplier-enlargement and Approximation of Unbounded Continuous Functions 被引量:1
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作者 郑成德 王仁宏 《Northeastern Mathematical Journal》 CSCD 2001年第2期231-235,共5页
By combining the classical appropriate functions “1, x, x 2” with the method of multiplier enlargement, this paper establishes a theorem to approximate any unbounded continuous functions with modified positive... By combining the classical appropriate functions “1, x, x 2” with the method of multiplier enlargement, this paper establishes a theorem to approximate any unbounded continuous functions with modified positive linear operators. As an example, Hermite Fejér interpolation polynomial operators are analysed and studied, and a general conclusion is obtained. 展开更多
关键词 positive linear operator approximation of unbounded continuous function method of multiplier enlargement Hermite Fejér interpolation polynomial operator
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DECOMPOSITION FOR BERS-ORLICZ SPACES
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作者 赵如汉 《Acta Mathematica Scientia》 SCIE CSCD 1995年第4期422-430,共9页
In this paper some decomposition theorems for classical weighted Orlicz spaces and Bers-Orlicz spaces are established. As applications of these decomposition theorems some estimates about the growth of the Taylor coef... In this paper some decomposition theorems for classical weighted Orlicz spaces and Bers-Orlicz spaces are established. As applications of these decomposition theorems some estimates about the growth of the Taylor coefficients of the functions in Bers-Orlicz spaces are given. 展开更多
关键词 weighted Orlicz spaces Bers-Orlicz spaces Fuchsian group Taylor coefficients DECOMPOSITION operator interpolation
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On the Cardinal Spline Interpolation Corresponding to Infinite Order Differential Operators
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作者 Chen Dirong Department of Mathematics Beijing Normal University Beijing,100875 and Center for Mathematical Sciences Zhejiang University Hangzhou,310027 China 《Acta Mathematica Sinica,English Series》 SCIE CSCD 1994年第3期315-324,共10页
This paper discusses some problems on the cardinal spline interpolation correspond- ing to infinite order differential operators.The remainder formulas and a dual theorem are es- tablished for some convolution classes... This paper discusses some problems on the cardinal spline interpolation correspond- ing to infinite order differential operators.The remainder formulas and a dual theorem are es- tablished for some convolution classes,where the kernels are PF densities.Moreover,the exact error of approximation of a convolution class with interpolation cardinal splines is determined. The exact values of average n-Kolmogorov widths are obtained for the convolution class. 展开更多
关键词 MATH On the Cardinal Spline interpolation Corresponding to Infinite Order Differential Operators LIM CHEN 卜成
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SUPERAPPROXIMATION PROPERTIES OF THE INTERPOLATION OPERATOR OF PROJECTION TYPE AND APPLICATIONS 被引量:1
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作者 Tie Zhang Yan-ping Lin R.J.Tait 《Journal of Computational Mathematics》 SCIE EI CSCD 2002年第3期277-288,共12页
Presents information on a study which analyzed superapproximation properties for the interpolation operator of projection type on two-dimensional domain. Discussion on the interpolation operator of projection type and... Presents information on a study which analyzed superapproximation properties for the interpolation operator of projection type on two-dimensional domain. Discussion on the interpolation operator of projection type and its superapproximation properties; Superconvergence of Ritz projection; Proof and applications of the superconveregence of Ritz-Volterra projection. 展开更多
关键词 interpolation operator of projection type finite element SUPERCONVERGENCE
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THE DEFECT ITERATION OF THE FINITE ELEMENT FOR ELLIPTIC BOUNDARY VALUE PROBLEMS AND PETROV-GALERKIN APPROXIMATION 被引量:4
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作者 Gao, JB Yang, YD Shih, TM 《Journal of Computational Mathematics》 SCIE CSCD 1998年第2期152-164,共13页
In this paper we introduce a Petrov-Galerkin approximation model to the solution of linear and semi-linear elliptic boundary value problems in which piecewise quadratic polynomial space and piecewise linear polynomial... In this paper we introduce a Petrov-Galerkin approximation model to the solution of linear and semi-linear elliptic boundary value problems in which piecewise quadratic polynomial space and piecewise linear polynomial space are used as the shape function space and the test function space, respectively. We prove that the approximation order of the standard quadratic finite element can be attained in this Petrov-Galerkin model. Based on the so-called 'contractivity' of the interpolation operator, we further prove that the defect iterative sequence of the linear finite element solution converge to the proposed Petrov-Galerkin approximate solution. 展开更多
关键词 Petrov-Galerkin approximation defect iteration correction interpolation operator
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Superconvergence analysis of fully discrete finite element methods for semilinear parabolic optimal control problems 被引量:3
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作者 Yuelong TANG Yanping CHEN 《Frontiers of Mathematics in China》 SCIE CSCD 2013年第2期443-464,共22页
We study the superconvergence property of fully discrete finite element approximation for quadratic optimal control problems governed by semilinear parabolic equations with control constraints. The time discretization... We study the superconvergence property of fully discrete finite element approximation for quadratic optimal control problems governed by semilinear parabolic equations with control constraints. The time discretization is based on difference methods, whereas the space discretization is done using finite element methods. The state and the adjoint state are approximated by piecewise linear functions and the control is approximated by piecewise constant functions. First, we define a fully discrete finite element approximation scheme for the semilinear parabolic control problem. Second, we derive the superconvergence properties for the control, the state and the adjoint state. Finally, we do some numerical experiments for illustrating our theoretical results. 展开更多
关键词 Superconvergence property quadratic optimal control problem fully discrete finite element approximation semilinear parabolic equation interpolate operator
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Superconvergence of tricubic block finite elements 被引量:2
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作者 LIU JingHong SUN HaiNa ZHU QiDing 《Science China Mathematics》 SCIE 2009年第5期959-972,共14页
In this paper, we first introduce interpolation operator of projection type in three dimen- sions, from which we derive weak estimates for tricubic block finite elements. Then using the estimate for the W 2, 1-seminor... In this paper, we first introduce interpolation operator of projection type in three dimen- sions, from which we derive weak estimates for tricubic block finite elements. Then using the estimate for the W 2, 1-seminorm of the discrete derivative Green's function and the weak estimates, we show that the tricubic block finite element solution uh and the tricubic interpolant of projection type Πh3u have superclose gradient in the pointwise sense of the L∞-norm. Finally, this supercloseness is applied to superconvergence analysis, and the global superconvergence of the finite element approximation is derived. 展开更多
关键词 block finite element interpolation operator of projection type SUPERCONVERGENCE SUPERCLOSENESS weak estimate discrete derivative Green’s function 65N30
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