Dilation Properties for Weighted Modulation Spaces
We give a sharp estimate on the norm of the scaling operator Uλf(x)=f(λx) acting on the weighted modulation spaces Ms,tp,q(ℝd). In particular, we recover and extend recent results by Sugimoto and Tomita in the unweighted case. As an application of our results, we estimate the growth in time of solut...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2012-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2012/145491 |
| Summary: | We give a sharp estimate on the norm of the scaling
operator Uλf(x)=f(λx) acting on the weighted modulation spaces Ms,tp,q(ℝd). In particular, we recover and extend recent results by Sugimoto and Tomita in the
unweighted case. As an application of our results, we estimate the growth in
time of solutions of the wave and vibrating plate equations, which is of interest
when considering the well-posedness of the Cauchy problem for these equations.
Finally, we provide new embedding results between modulation and Besov spaces. |
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| ISSN: | 0972-6802 1758-4965 |