Sharpness of some properties of Wiener amalgam and modulation spaces

Abstract

We prove sharp estimates for the dilation operator $f(x)⟼f(\lambda x)$, when acting on Wiener amalgam spaces $W(L^p,L^q)$. Scaling arguments are also used to prove the sharpness of the known convolution and pointwise relations for modulation spaces $M^{p,q}$, as well as the optimality of an estimate for the Schrödinger propagator on modulation spaces.

12 pages