Wiener Amalgam Spaces and Invariance Properties
(new results about the Fofana spaces (L^q,l^p)^{\alpha})

We will start to discuss a family of function spaces derived from the Wiener amalgam spaces W(L^q,l^p), which have been introduced by I. Fofana a while ago and studied in a series of papers, one of the most recent contributions is this one:
Bérenger Kpata and Ibrahim Fofana [fokp14]
Isomorphism between Sobolev spaces and Bessel potential spaces in the setting of Wiener amalgam spaces. Commun. Math. Anal., Vol.16 No.2, (2014) p.57--73

One can show that they are subspace of Wiener amalgams with a particular dilation behaviour. It was known that they are dual spaces, but we could determine the predual and provide an atomic characterization of the predual.

The ideas are related to methods about minimal invariant spaces developed for the proof of Tauberian theorems in Hans G. Feichtinger [fe88]: An elementary approach to Wiener's third Tauberian theorem for the Euclidean n-space, in "Symposia Math.", Analisa Armonica, Vol.XXIX (1988) [Cortona] p.267--301 resp. in
Hans G. Feichtinger and Georg Zimmermann [fezi02]
An exotic minimal Banach space of functions
Math. Nachr., Vol.239-240 (2002) p.42-61.

THIS TALK was given as a chalk talk. Hence there are no slides for download.

Many details are found at
http://univie.ac.at/nuhag-php/dateien/talks/401_FeiBremTST.pdf