A note on equivalence of anchored and ANOVA spaces; lower bounds

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• 作者：Peter Kritzer^a ; ^{peter.kritzer@oeaw.ac.at} ; Friedrich Pillichshammer^b ; ^{friedrich.pillichshammer@jku.at} ; G.W. Wasilkowski^c ; ^{greg@cs.uky.edu}
• 关键词：Embeddings ; Weighted function spaces ; Anchored decomposition ; ANOVA decomposition ; Equivalence of norms
• 刊名：Journal of Complexity
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：38
• 期：Complete
• 页码：31-38
• 全文大小：402 K
• 卷排序：38

文摘

We provide lower bounds for the norms of embeddings between γ-weighted anchored and ANOVA spaces of ss-variate functions on [0,1]s[0,1]s with mixed partial derivatives of order one bounded in LpLp norm (p∈[1,∞]p∈[1,∞]). In particular we show that the norms behave polynomially in ss for specific instances of finite order weights and finite diameter weights  , and increase faster than any polynomial in ss for product order-dependent weights.