On Approximation of Function Classes in Lorentz Spaces with Anisotropic Norm
On Approximation of Function Classes in Lorentz Spaces with Anisotropic Norm
摘要
In this paper, Lorentz space of functions of several variables and Besov＇s class are considered. We establish an exact approximation order of Besov＇s class by partial sums of Fourier＇s series for multiple trigonometric system.
In this paper, Lorentz space of functions of several variables and Besov＇s class are considered. We establish an exact approximation order of Besov＇s class by partial sums of Fourier＇s series for multiple trigonometric system.
参考文献28
-
1G. Akishev, Approximation of functions classes in spaces mixed norm, Math. Sbomik, 197(8) (2006),17-40, (http://www .mathnet .ru/msb).
-
2G. Akishev, On orders of approximation of function classes in Lorentz spaces with anisotropic norm, Math. Notes, 81(1) (2007),3-14, (http://www . mathnet. ru/mz).
-
3T. I. Amanov, Spaces of differentiable functions with dominant mixed derivative, Alma-Ata, 1976, in Russian.
-
4K. I. Babenko, Approximation by trigonometric polynomials in a certain class of periodic functions of several variables, Dokl. Akad. Nauk SSSR, 132(5) (1960),982-985.
-
5D. B Bazarkhanov, Wavelet approximation and Fourier widths of classes of periodic functions of several variables: I, Trudy Math. Inst. Steklov, 269 (2010), 8-30.
-
6E. S. Belinski, Approximation of functions of several variables by trigonometric polynomials with given number of harmonics, and estimates of s-entropy, Anal. Math., 15 (1989),67-74.
-
7A. P. Blozinski, Multivariate rearrangements and Banach function spaces with mixed norms, Trans. Amer. Math. Soc., 263 (1981), 146-167.
-
8Ya. S. Bugrov, Approximation of classes of functions with dominant mixed derivative, Math. Bb.,64 (1964),410-418, (http://www.mathnet.ru/msb). (in Russian).
-
9A. R. DeVore, P. Petrushev and V. N. Temlyakov, Multivariate trigonometric approximation with frequencies from the hyperbolic cross, Mat. Zametki, 56(3) (1994),36-63, English Translation in Math. Notes, 56, (http://www.mathnet.ru/mz).
-
10R. A. DeVore, S. V. Konyagin and V. N. Temlyakov, Hiperbolic wavelet approximation, Construc. Approx., 14 (1998), 1-26.
-
1张娟,杨金龙,独力.洛伦兹空间中的双调和伪黎曼超曲面（英文）[J].贵州大学学报（自然科学版）,2015,32(6):4-8.
-
2ChenJiecheng ZhuXiangrong.SOME PROPERTIES OF Λ_ω~P(X,μ)[J].Analysis in Theory and Applications,2005,21(1):65-72.
-
3江蓉,王守中.一类三角系统的匹配数与点独立集数[J].西南师范大学学报（自然科学版）,2009,34(1):20-23. 被引量：3
-
4王守中,江蓉.三角系统T_n的匹配数与点独立集数[J].西南师范大学学报（自然科学版）,2010,35(1):19-22. 被引量：4
-
5Hong Liang LI.Self-similar Solutions of the Navier–Stokes Equations on Weak Weighted Lorentz Spaces[J].Acta Mathematica Sinica,English Series,2015,31(1):44-60.
-
6Hongliang LI,Jiecheng CHEN.Convolutions, Tensor Products and Multipliers of the Orlicz-Lorentz Spaces[J].Chinese Annals of Mathematics,Series B,2015,36(3):467-484.
-
7张知学,高瑞.The Killing Forms of Lie Triple Systems[J].Journal of Mathematical Research and Exposition,2009,29(4):745-752.
-
8黎镇琦,谢显华.洛伦兹空间型H_1^(n+1) 和S_1^(n+1)中的类空等参超曲面[J].南昌大学学报（理科版）,2004,28(2):113-117. 被引量：3
-
9许贵桥,余纯武.THE GEL'FAND n-WIDTHS OF MULTIVARIATE PERIODIC BESOV CLASSES[J].Acta Mathematica Scientia,2003,23(3):399-404.
-
10ZHANG Duan,TARN Tzyh Jong,HE XiongXiong,ZOU Tao.Geometric characterization of multi-input lower-triangular forms[J].Science China(Information Sciences),2011,54(9):1868-1882.
