Design and properties of wave packet smoothness spaces
Functional Analysis
2019-04-25 v1
Abstract
We introduce a family of quasi-Banach spaces - which we call wave packet smoothness spaces - that includes those function spaces which can be characterised by the sparsity of their expansions in Gabor frames, wave atoms, and many other frame constructions. We construct Banach frames for and atomic decompositions of the wave packet smoothness spaces and study their embeddings in each other and in a few more classical function spaces such as Besov and Sobolev spaces.
Keywords
Cite
@article{arxiv.1904.10687,
title = {Design and properties of wave packet smoothness spaces},
author = {Dimitri Bytchenkoff and Felix Voigtlaender},
journal= {arXiv preprint arXiv:1904.10687},
year = {2019}
}
Comments
accepted for publication in Journal de Math\'ematiques Pures et Appliqu\'ees