Entropy numbers of functions on [−1,1] with Jacobi weights

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• 作者：Kai Wang ; ^{cnuwangk@163.com" class="auth_mail" title="E-mail the corresponding author} ; Yali Wang ^{2284690983@qq.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Entropy numbers ; Weighted Sobolev space ; Gaussian quadrature formulae
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：445
• 期：1
• 页码：985-997
• 全文大小：351 K

文摘

We study the entropy numbers of weighted Sobolev classes $B{W}_{p,\alpha ,\beta }^r$ in L_q,α,β$L_{q,\alpha ,\beta }$, where L_q,α,β,1≤q≤∞$L_{q,\alpha ,\beta },1\le q\le \infty$ denotes the weighted L_q$L_q$ space on [−1,1]$[-1,1]$ with respect to weight $w_{\alpha ,\beta }(x):={(1-x)}^{\alpha }{(1+x)}^{\beta },\alpha ,\beta >-1/2$. Exact orders of the entropy numbers are obtained for all 1≤p,q≤∞$1\le p,q\le \infty$ and α,β>−1/2$\alpha ,\beta >-1/2$.