Math. Model. Nat. Phenom.
Volume 8, Number 1, 2013Harmonic analysis
|Page(s)||175 - 192|
|Published online||28 January 2013|
Boundedness of Pseudo-Differential Operators on Lp, Sobolev and Modulation Spaces
1 Department of Mathematics and
Statistics, Queen’s University, Kingston, Ontario
2 School of Engineering and Science, Jacobs University, 28759 Bremen, Germany
∗ Corresponding author. E-mail: firstname.lastname@example.org
We introduce new classes of modulation spaces over phase space. By means of the Kohn-Nirenberg correspondence, these spaces induce norms on pseudo-differential operators that bound their operator norms on Lp–spaces, Sobolev spaces, and modulation spaces.
Mathematics Subject Classification: 47G30 / 42B35 / 35S05 / 46E35
Key words: pseudo-differential operators / modulation spaces / Sobolev spaces / short–time Fourier transforms
© EDP Sciences, 2013
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