NASep 19, 2018
Embeddings for Infinite-Dimensional Integration and $L_2$-Approximation with Increasing SmoothnessM. Gnewuch, M. Hefter, A. Hinrichs et al.
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.