Sharpness of some properties of Wiener amalgam and modulation spaces

Details Sharpness of some properties of Wiener amalgam and modulation spaces Sharpness of some properties of Wiener amalgam and modulation spaces

2008-03-21

arxiv.org/abs/0803.3140v1

Mathematics

Functional Analysis

12 pages

Scientific paper

We prove sharp estimates for the dilation operator $f(x)\longmapsto f(\lambda
x)$, 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 Schr\"odinger propagator on modulation spaces.

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