# Function Spaces and Invariance Properties

Hans G. Feichtinger

given at  Prag (13.07.18 11:30)
id:  3588
length:  25min
status:
type:
atomic decompositions (Coifman-Weiss, 1977) we can mention the work on the Segal algebra $\SORdN$ in the context of Gabor analysis , but also the proof of Wiener's Third Tauberian Theorem (see \cite{fe88}) for functions of bounded $p$-means on $\Rst^d$ (Wiener did the case $d=1, p=2$ in his book of 1933.
We will also present some known results concerning the {\it Fofana spaces} $(\Lqsp,\lpsp)^{\alpha}$. These spaces are defined as subspaces of Wiener Amalgam spaces $\Wsp(\Lqsp,\lpsp)(\Rdst)$, for $1 \leq p < \alpha < q \leq \infty$ (otherwise they are trivial). In particular we are able to describe them as dual Banach spaces and provide atomic characterizations of the predual.