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
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