  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.
