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...
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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 |
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doaj-04a111d3815749afa47e3e86a0c7554b2020-11-24T23:04:55ZengHindawi LimitedJournal of Function Spaces and Applications0972-68021758-49652012-01-01201210.1155/2012/145491145491Dilation Properties for Weighted Modulation SpacesElena Cordero0Kasso A. Okoudjou1Department of Mathematics, University of Torino, Via Carlo Alberto 10, 10123 Torino, ItalyDepartment of Mathematics, University of Maryland, College Park, MD 20742, USAWe 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.http://dx.doi.org/10.1155/2012/145491 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Elena Cordero Kasso A. Okoudjou |
| spellingShingle |
Elena Cordero Kasso A. Okoudjou Dilation Properties for Weighted Modulation Spaces Journal of Function Spaces and Applications |
| author_facet |
Elena Cordero Kasso A. Okoudjou |
| author_sort |
Elena Cordero |
| title |
Dilation Properties for Weighted Modulation Spaces |
| title_short |
Dilation Properties for Weighted Modulation Spaces |
| title_full |
Dilation Properties for Weighted Modulation Spaces |
| title_fullStr |
Dilation Properties for Weighted Modulation Spaces |
| title_full_unstemmed |
Dilation Properties for Weighted Modulation Spaces |
| title_sort |
dilation properties for weighted modulation spaces |
| publisher |
Hindawi Limited |
| series |
Journal of Function Spaces and Applications |
| issn |
0972-6802 1758-4965 |
| publishDate |
2012-01-01 |
| description |
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. |
| url |
http://dx.doi.org/10.1155/2012/145491 |
| work_keys_str_mv |
AT elenacordero dilationpropertiesforweightedmodulationspaces AT kassoaokoudjou dilationpropertiesforweightedmodulationspaces |
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1725628466785681408 |