Embeddings for Infinite-Dimensional Integration and $L_2$-Approximation with Increasing Smoothness

Abstract

We study integration and $L_2$-approximation on countable tensor products of function spaces of increasing smoothness. We obtain upper and lower bounds for the minimal errors, which are sharp in many cases including, e.g., Korobov, Walsh, Haar, and Sobolev spaces. For the proofs we derive embedding theorems between spaces of increasing smoothness and appropriate weighted function spaces of fixed smoothness.

References in corpus (2)

• Embeddings of Weighted Hilbert Spaces and Applications to Multivariate and Infinite-Dimensional Integration
• Equivalence of Weighted Anchored and ANOVA Spaces of Functions with Mixed Smoothness of Order one in $L_p$

Cited by in corpus (5)

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• Infinite-dimensional integration and $L^2$-approximation on Hermite spaces
• How anisotropic mixed smoothness affects the decay of singular numbers of Sobolev embeddings
• Infinite-Variate $L^2$-Approximation with Nested Subspace Sampling
• Equivalence between Sobolev spaces of first-order dominating mixed smoothness and unanchored ANOVA spaces on ${\mathbb{R}}^d$