On equivalence of weighted anchored and ANOVA spaces of functions with mixed smoothness of order one in \(L_1\) or \(L_\infty\)

DOI10.1016/j.jco.2015.07.001zbMath1342.46032OpenAlexW1038389461MaRDI QIDQ895981

Klaus Ritter, Mario Hefter, Grzegorz W. Wasilkowski

Publication date: 11 December 2015

Published in: Journal of Complexity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jco.2015.07.001

zbMATH Keywords

embeddingsweighted function spacesANOVA decompositiontractabilityanchored decompositionequivalence of norms

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30)

Related Items (14)

Stable splittings of Hilbert spaces of functions of infinitely many variables ⋮ Very low truncation dimension for high dimensional integration under modest error demand ⋮ A note on equivalence of anchored and ANOVA spaces; lower bounds ⋮ Equivalence of weighted anchored and ANOVA spaces of functions with mixed smoothness of order one in \(L_p\) ⋮ Equivalence between Sobolev spaces of first-order dominating mixed smoothness and unanchored ANOVA spaces on ℝ^{𝕕} ⋮ Small superposition dimension and active set construction for multivariate integration under modest error demand ⋮ Embeddings of weighted Hilbert spaces and applications to multivariate and infinite-dimensional integration ⋮ Optimal algorithms for doubly weighted approximation of univariate functions ⋮ Truncation Dimension for Function Approximation ⋮ Truncation dimension for linear problems on multivariate function spaces ⋮ Quasi-Monte Carlo and \(\varepsilon\)-truncation dimension in ANOVA spaces ⋮ Embeddings for infinite-dimensional integration and \(L_2\)-approximation with increasing smoothness ⋮ \( \varepsilon \)-superposition and truncation dimensions in average and probabilistic settings for \(\infty \)-variate linear problems ⋮ On quasi-Monte Carlo methods in weighted ANOVA spaces

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