Regularity, Decay, and Best Constants for Dispersive Equations

We show that the Strichartz L2w(L2)-estimates for solutions to the (pseudo-) differential equations−Δxu=i∂tu and −Δx +1 u=i∂tu are equivalent. A necessary and sufficient condition for decay and regularity for solutions to the equationϕ(−Δx) u=i∂tu is given.