We study classes of pseudodifferential operators which are bounded on large collections of modulation spaces. The conditions on the operators are stated in terms of the L p,q estimates for the continuous Gabor transforms of their symbols. In particular, we show how these classes are related to the c
Boundedness for pseudodifferential operators on multivariate α-modulation spaces
✍ Scribed by Lasse Borup; Morten Nielsen
- Book ID
- 107382358
- Publisher
- Springer Netherlands
- Year
- 2006
- Tongue
- English
- Weight
- 294 KB
- Volume
- 44
- Category
- Article
- ISSN
- 0004-2080
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📜 SIMILAR VOLUMES
## Abstract We give a characterization of __d__‐dimensional modulation spaces with moderate weights by means of the __d__‐dimensional Wilson basis. As an application we prove that pseudodifferential operators with generalized Weyl symbols are bounded on these modulation spaces.
We establish a connection between certain classes of pseudodifferential operators and Hille᎐Tamarkin operators. As an application, we find the conditions that guarantee compactness and summability of the eigenvalues of pseudodifferential operators acting on the modulation spaces M p, p .