We prove sharp estimates for the dilation operator f(x)⟼f(λx), when acting on Wiener amalgam spaces W(Lp,Lq). Scaling arguments are
also used to prove the sharpness of the known convolution and pointwise
relations for modulation spaces Mp,q, as well as the optimality of an
estimate for the Schr\"odinger propagator on modulation spaces.Comment: 12 page