Continuity Properties for Modulation Spaces, with Applications to Pseudo-differential Calculus-I
| Document type: | Journal Articles |
|---|---|
| Article type: | Original article |
| Peer reviewed: | Yes |
| Author(s): | Joachim Toft |
| Title: | Continuity Properties for Modulation Spaces, with Applications to Pseudo-differential Calculus-I |
| Journal: | Journal of the Functional Analysis |
| Year: | 2004 |
| Volume: | 207 |
| Issue: | 2 |
| Pagination: | 399-429 |
| ISSN: | 0022-1236 |
| Publisher: | Elsevier |
| City: | San Diego, USA |
| ISI number: | 000188778300007 |
| Organization: | Blekinge Institute of Technology |
| Department: | School of Engineering - Dept. Mathematics and Science (Sektionen för teknik – avd. för matematik och naturvetenskap) School of Engineering S- 371 79 Karlskrona +46 455 38 50 00 http://www.tek.bth.se/ |
| Language: | English |
| Abstract: | Let M-p,M- q denote the modulation space with parameters p, q is an element of [1, infinity]. If 1/p(1) + 1/p(2) = 1 + 1/p(0) and 1/q(1) + 1/q(2) = 1/q(0), then it is proved that M-p1,M- q1 * M-p2,M- q2 subset of M-p0,M- q0. The result is used to get inclusions between modulation spaces, Besov spaces and Schatten classes in calculus of psido (pseudo-differential operators), and to extend the definition of Toeplitz operators. We also discuss continuity of ambiguity functions and psido in the framework of modulation spaces. |
| Subject: | Mathematics\Analysis |
| Keywords: | modulation spaces, pseudo-differential operators, embeddings, convolution, Toeplitz operators, Schatten classes |
