Approximation of smooth functions on compact two-point homogeneous spaces
Approximation of smooth functions on compact two-point homogeneous spaces
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DOI：
10.1016/j.jfa.2004.10.005
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发表时间：
2005-03
影响因子：
1.7
通讯作者：
G. Brown;F. Dai
中科院分区：
文献类型：
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作者：
G. Brown;F. Dai
在紧致两点齐性空间（CTPHS）上建立了Sobolev类Bpr，（r>0，1 <$p <$∞）的Kolmogorov n-宽度dn（Bpr，Lq）和线性n-宽度δn（Bpr，Lq），（1 <$q <$∞）的估计. Bordin等（J. Funct. Anal. 202（2）（2003）307）。本文给出了所有剩余（p，q）的dn（Bpr，Lq）和δn（Bpr，Lq）的锐阶.我们的证明是基于CTPHS上的正体积公式和Marcinkiewicz-Zygmund型不等式。
Estimates of Kolmogorov n-widths dn(Bpr,Lq) and linear n-widths δn(Bpr,Lq), (1⩽q⩽∞) of Sobolev's classes Bpr, (r>0, 1⩽p⩽∞) on compact two-point homogeneous spaces (CTPHS) are established. For part of (p,q)∈[1,∞]×[1,∞], sharp orders of dn(Bpr,Lq) or δn(Bpr,Lq) were obtained by Bordin et al. (J. Funct. Anal. 202(2) (2003) 307). In this paper, we obtain the sharp orders of dn(Bpr,Lq) and δn(Bpr,Lq) for all the remaining (p,q). Our proof is based on positive cubature formulas and Marcinkiewicz–Zygmund-type inequalities on CTPHS.