We study the notion of molecules in coorbit spaces. The main result states that if an operator, originally defined on an appropriate space of test functions, maps atoms to molecules, then it can be extended to a bounded operator on coorbit spaces. For time-frequency molecules we recover some boundedness results on modulation spaces, for time-scale molecules we obtain the boundedness on homogeno...

In this paper we introduce a notion of multilinear localization operators. By reinterpreting these operators as multilinear Kohn-Nirenberg pseudodifferential operators, we prove that these multilinear localization operators are bounded on products of modulation spaces. In particular, by assuming that the symbols of the localization operators belong to the largest modulation space, i.e., M , we ...

We study the local-in-time regularity of the Brownian motion with respect to localized variants of modulation spaces M s and Wiener amalgam spaces W p,q s . We show that the periodic Brownian motion belongs locally in time to M s (T) and W p,q s (T) for (s − 1)q < −1, and the condition on the indices is optimal. Moreover, with the Wiener measure μ on T, we show that (M s (T), μ) and (W p,q s (T...