We introduce spaces of exponential constructible functions in the motivic
setting for which we construct direct image functors in the absolute and
relative cases. This allows us to define a motivic Fourier transformation for
which we get various inversion statements. We define also motivic
Schwartz-Bruhat spaces on which motivic Fourier transformation induces an
isomorphism. Our motivic integrals specialize to non archimedian integrals. We
give a general transfer principle comparing identities between functions
defined by integrals over local fields of characteristic zero, resp. positive,
having the same residue field. Details of constructions and proofs will be
given elsewhere.Comment: 10 page
