Dilation Properties for Weighted Modulation Spaces
Abstract
We give a sharp estimate on the norm of the scaling operatorUλf(x)=f(λx)acting on the weighted modulation spacesMs,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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jan 01, 2012
- Source ID
- 10.1155/2012/145491
Entities
People
- Elena Cordero
- Kasso A. Okoudjou
Organizations
- Office of Naval Research
- University of Maryland
- University of Turin