Embeddings of Weighted Hilbert Spaces and Applications to Multivariate and Infinite-Dimensional Integration

TL;DR

This paper investigates embeddings and norm estimates for tensor products of weighted reproducing kernel Hilbert spaces, providing new results for multivariate and infinite-dimensional integration and approximation problems.

Contribution

It introduces a transfer principle for tractability studies and derives new integration results for weighted tensor product Sobolev spaces with various norms.

Findings

New norm estimates for tensor product spaces

Transfer principle for tractability analysis

Enhanced integration results for Sobolev spaces

Abstract

We study embeddings and norm estimates for tensor products of weighted reproducing kernel Hilbert spaces. These results lead to a transfer principle that is directly applicable to tractability studies of multivariate problems as integration and approximation, and to their infinite-dimensional counterparts. In an application we consider weighted tensor product Sobolev spaces of mixed smoothness of any integer order, equipped with the classical, the anchored, or the ANOVA norm. Here we derive new results for multivariate and infinite-dimensional integration.