On equivalence of weighted anchored and ANOVA spaces of functions with mixed smoothness of order one in or

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• 作者：M. Hefter^a ; ^{hefter@mathematik.uni-kl.de" class="auth_mail" title="E-mail the corresponding author} ; K. Ritter^a ; ^{ritter@mathematik.uni-kl.de" class="auth_mail" title="E-mail the corresponding author} ; G.W. Wasilkowski^b ; ^{greg@cs.uky.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Embeddings ; Weighted function spaces ; Anchored decomposition ; ANOVA decomposition ; Equivalence of norms ; Tractability
• 刊名：Journal of Complexity
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：32
• 期：1
• 页码：1-19
• 全文大小：452 K

文摘

We consider weighted anchored and ANOVA spaces of functions with mixed first order partial derivatives bounded in g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0885064X15000643&_mathId=si1.gif&_user=111111111&_pii=S0885064X15000643&_rdoc=1&_issn=0885064X&md5=cde213cfccd88dbddeea1c65cfdb39bd" title="Click to view the MathML source">L₁gif" overflow="scroll">L1 or g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0885064X15000643&_mathId=si2.gif&_user=111111111&_pii=S0885064X15000643&_rdoc=1&_issn=0885064X&md5=5b65d8582d3b48276650129ff42491e2" title="Click to view the MathML source">L_∞gif" overflow="scroll">L∞ norms. We provide conditions on the weights under which the corresponding spaces have equivalent norms with constants independent of, or only polynomially dependent on the number of variables.