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

作者：Kritzer Peter; Pillichshammer Friedrich^*; Wasilkowski G W

来源：Journal of Complexity, 2017, 38: 31-38.

DOI：10.1016/j.jco.2016.06.001

• Embeddings
• Weighted function spaces
• Anchored decomposition
• ANOVA decomposition
• Equivalence of norms

We provide lower bounds for the norms of embeddings between gamma-weighted anchored and ANOVA spaces of s-variate functions on [0, 1](S) with mixed partial derivatives of order one bounded in 4, norm (p is an element of [1, infinity]). In particular we show that the norms behave polynomially in s for specific instances of finite order weights and finite diameter weights, and increase faster than any polynomial in s for product order-dependent weights.

• 出版日期2017-2