We prove sharp estimates for the dilation operator 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 Schroedinger propagator on modulation spaces.
Sharpness of some properties of Wiener amalgam and modulation spaces
CORDERO, Elena;
2009-01-01
Abstract
We prove sharp estimates for the dilation operator 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 Schroedinger propagator on modulation spaces.
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