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Boundedness of pseudodifferential operators on modulation spaces

✍ Scribed by Wojciech Czaja

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
94 KB
Volume
284
Category
Article
ISSN
0022-247X

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✦ Synopsis

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 class of operators of Gröchenig and Heil, which is bounded on all modulation spaces.

📜 SIMILAR VOLUMES

The Boundedness of Pseudodifferential Op
The Boundedness of Pseudodifferential Operators on Modulation Spaces
✍ Kazuya Tachizawa 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 539 KB

## 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.

Pseudodifferential Operators on Modulati
Pseudodifferential Operators on Modulation Spaces
✍ Demetrio Labate 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 118 KB

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 .