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

Peter Kritzer, Friedrich Pillichshammer, G. W. Wasilkowski

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


We provide lower bounds for the norms of embeddings between γ-weighted anchored and ANOVA spaces of s-variate functions on [0,1]s with mixed partial derivatives of order one bounded in Lp norm (p∈[1,∞]). 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.

Original languageEnglish
Pages (from-to)31-38
Number of pages8
JournalJournal of Complexity
StatePublished - Feb 1 2017

Bibliographical note

Publisher Copyright:
© 2016 Elsevier Inc.


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

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Statistics and Probability
  • Numerical Analysis
  • General Mathematics
  • Control and Optimization
  • Applied Mathematics


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