In this article,we study multivariate approximation defined over weighted anisotropic Sobolev spaces which depend on two sequences a={a j}j≥1 and b={b j}j≥1 of positive numbers.We obtain strong equivalences of the a...In this article,we study multivariate approximation defined over weighted anisotropic Sobolev spaces which depend on two sequences a={a j}j≥1 and b={b j}j≥1 of positive numbers.We obtain strong equivalences of the approximation numbers,and necessary and sufficient conditions on a,b to achieve various notions of tractability of the weighted anisotropic Sobolev embeddings.展开更多
We study sufficient conditions on radial and non-radial weight functions on the upper half-plane that guarantee norm approximation of functions in weighted Bergman,weighted Dirichlet,and weighted Besov spaces on the u...We study sufficient conditions on radial and non-radial weight functions on the upper half-plane that guarantee norm approximation of functions in weighted Bergman,weighted Dirichlet,and weighted Besov spaces on the upper half-plane by dilatations and eventually by analytic polynomials.展开更多
We prove some approximation properties of generalized Meyer-Konig and Zeller operators for differentiable functions in polynomial weighted spaces. The results extend some results proved in [1-3,7-16].
In this paper, we investigate the order of approximation by reproducing kernel spaces on （-1, 1） in weighted L^p spaces. We first restate the translation network from the view of reproducing kernel spaces and then c...In this paper, we investigate the order of approximation by reproducing kernel spaces on （-1, 1） in weighted L^p spaces. We first restate the translation network from the view of reproducing kernel spaces and then construct a sequence of approximating operators with the help of Jacobi orthogonal polynomials, with which we establish a kind of Jackson inequality to describe the error estimate. Finally, The results are used to discuss an approximation problem arising from learning theory.展开更多
We discuss the Banach space structure of the fractional order weighted Fock-Sobolev spaces fPα,s, mainly include giving some growth estimates for Fock-Sobolev functions and approximating them by a sequence of ＇nice...We discuss the Banach space structure of the fractional order weighted Fock-Sobolev spaces fPα,s, mainly include giving some growth estimates for Fock-Sobolev functions and approximating them by a sequence of ＇nice＇ functions in two different ways.展开更多
Abstract： We characterize the boundedness and compactness of weighted compo-sition operators among some Fock-Sobolev spaces. We also estimate the norm and essential norm of these operators. Furthermore, we discuss ...Abstract： We characterize the boundedness and compactness of weighted compo-sition operators among some Fock-Sobolev spaces. We also estimate the norm and essential norm of these operators. Furthermore, we discuss the duality spaces of Fock-Sobolev spaces Fs^p,mwhen 0 〈 p 〈∞.展开更多
The aim of this paper is to set up the weighted norm inequalities for commutators generated by approximate identities from weighted Lebesgue spaces into weighted Morrey spaces
基金the National Natural Science Foundation of China(11671271)the Natural Science Foundation of Beijing Municipality(1172004).
文摘In this article,we study multivariate approximation defined over weighted anisotropic Sobolev spaces which depend on two sequences a={a j}j≥1 and b={b j}j≥1 of positive numbers.We obtain strong equivalences of the approximation numbers,and necessary and sufficient conditions on a,b to achieve various notions of tractability of the weighted anisotropic Sobolev embeddings.
文摘We study sufficient conditions on radial and non-radial weight functions on the upper half-plane that guarantee norm approximation of functions in weighted Bergman,weighted Dirichlet,and weighted Besov spaces on the upper half-plane by dilatations and eventually by analytic polynomials.
文摘We prove some approximation properties of generalized Meyer-Konig and Zeller operators for differentiable functions in polynomial weighted spaces. The results extend some results proved in [1-3,7-16].
基金The research is supported by the National Natural Science Foundation under Grant No. 10471130 and the Zhejiang Province Science Foundation under Grant No. Y604003. Acknowledgements The author thanks the referees for giving valuable comments on this paper which make him rewrite this paper in a better form.
文摘In this paper, we investigate the order of approximation by reproducing kernel spaces on （-1, 1） in weighted L^p spaces. We first restate the translation network from the view of reproducing kernel spaces and then construct a sequence of approximating operators with the help of Jacobi orthogonal polynomials, with which we establish a kind of Jackson inequality to describe the error estimate. Finally, The results are used to discuss an approximation problem arising from learning theory.
基金Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant Nos. 11501136, 11271092）, the Key Discipline Construction Project of Subject Groups Focus on Mathematics and Information Science in the Construction Project of the High-Level University of Guangdong Province （No. 4601-2015）, and the Project for the New Talent of Guangzhou University （No. HL02-1517）.
文摘We discuss the Banach space structure of the fractional order weighted Fock-Sobolev spaces fPα,s, mainly include giving some growth estimates for Fock-Sobolev functions and approximating them by a sequence of ＇nice＇ functions in two different ways.
基金The NSF(11501136,11271092)of Chinathe Key Discipline Construction Project of Subject Groups Focus on Mathematics+1 种基金Information Science in the Construction Project(4601-2015)of the High-level University of Guangdong Provincethe Project(HL02-1517)for the New Talent of Guangzhou University
文摘Abstract： We characterize the boundedness and compactness of weighted compo-sition operators among some Fock-Sobolev spaces. We also estimate the norm and essential norm of these operators. Furthermore, we discuss the duality spaces of Fock-Sobolev spaces Fs^p,mwhen 0 〈 p 〈∞.
基金supported by the NSF(11271175) of Chinathe NSF(ZR2012AQ026) of Shandong Province
文摘The aim of this paper is to set up the weighted norm inequalities for commutators generated by approximate identities from weighted Lebesgue spaces into weighted Morrey spaces
