Continuity properties for modulation spaces, with applications to pseudo-differential calculus - I

Journal of Functional Analysis

Volumn 207, Issue 2, 2004, Pages 399-429

  Toft, Joachim ^a  

^a BLEKINGE INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

Convolution; Embeddings; Modulation spaces; Pseudo differential operators; Schatten classes; Toeplitz operators

Indexed keywords

EID: 1242294479     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jfa.2003.10.003     Document Type: Article

References (36)

1. J. Bergh, J. Löfsaröm, Interpolation Spaces, An Introduction, Springer, Berlin, Heidelberg, New York. 1976.
2. 2 estimates for pseudodifferential operators, Ann. Scuola Norm, Sup. Pisa Cl. Sci 22 (4) (1995) 155-183.
3. A. Boukhemair, Remarks on a Wiener type pseudodifferential algebra and Fourier integral operators, Math. Res. L. 4 (1997) 53-67.
4. 2 estimates for Weyl quantization, J. Funct. Anal. 165 (1999) 173-204.
5. E. Cordero, K. Gr̈ochenig, Time frequency analysis of localization operators, preprint, 2002.
6. W. Czaja, Z. Rzeszotnik, Pseudodifferential operators and Gabor frames: spectral asymptotics, Math. Nachr. 233/234 (2002) 77-88.
7. M. Dimassi, J. Sjöstrand. Spectral asymptotics in the semi-classical limit, in: London Mathematical Society, Lecture Note Series, Vol. 268, Cambridge University Press, Cambridge, New York, Melbourne, Madrid, 1999.
8. H.G. Feichtinger. Banach spaces of distributions of Wiener's type and interpolation, in: P. Butzer, B.Sz. Nagy, E. Görlich (Eds. . Proc. Conf. Oberwolfach, Functional Analysis and Approximation, August 1980, Int. Ser. Num. Math., Vol. 69, Birkhäuser-Verlag, Basel, Boston, Stuttgart, 1981. pp. 153-165.
9. H.G. Feichtinger, Banach convolution algebras of Wiener's type, in: Proceedings on Functions, Series. Operators in Budapest, Colloquia Math. Soc. J. Bolyai, North-Holland, Amsterdam, Oxford, New York. 1980.
10. H.G. Feichtinger, Modulation spaces on locally compact abelian groups, Technical Report. University of Vienna, Vienna, 1983.
11. H.G. Feichtinger, P. Gröbner, Banach spaces of distributions defined by decomposition methods, I, Math. Nachr. 123 (1985) 97-120.
12. H.G. Feichtinger, K.H. Gröchenig, Banach spaces related to integrable group representations and their atomic decompositions, I, J. Funct. Anal. 86 (1989) 307-340.
13. H.G. Feichtinger, K.H. Gröchenig, Banach spaces related to integrable group representations and their atomic decompositions, II, Monatsh. Math. 108 (089) 129-148.
14. H.G. Feichtinger, K.H. Gröchenig. Gabor frames and time-frequency analysis of distributions, J. Funct. Anal. 146 (2) (1997) 464-495.
15. H.G. Feichtinger, T. Strohmer (Fds.). Gabor Analysis and Algorithms, Theory and Applications, Birkhäuser, Boston, Basel, Berlin, 1998.
16. G.B. Folland, Harmonic Analysis in Phase Space, Princeton University Press, Princeton, 1989.
17. P. Gröbner, Banachräume Glatter Funktionen und Zerlegungsmethoden, Thesis, University of Vienna. Vienna, 1983.
18. K.H. Gröchenig, Describing functions: atomic decompositions versus frames, Monatsh. Math. 112 (1991) 1-42.
19. K.H. Gröchenig, Foundations of Time-Frequency Analysis, Birkhäuser, Boston, 2001.
20. K.H. Gröchenig, C. Heil, Modulation spaces and pseudo-differential operators, Integral Equations Operator Theory 34 (4) (1999) 439-457.
21. K.H. Gröchenig, C. Heil, private communications.
22. L. Hörmander. The Analysis of Linear Partial Differential Operators, Vol. I, III, Springer. Berlin, Heidelberg, New York, Tokyo, 1983, 1985.
23. C. Heil. J. Ramanathan, P. Topiwala, Singular values of compact pseuodifferential operators, J. Funct. Anal. 150 (2) (1997) 426-452.
24. Z. He, M.W. Wong, Localization operators associated to square integrable group representations, Panamer. Math. J. 6 (1) (1996) 93-104.
25. D. Labate, Pseudodifferential operators on modulation spaces. J. Math. Anal. Appl. 262 (2001) 242-255.
26. K.A. Okoudjou, Embeddings of some classical Banach spaces into modulation spaces, preprint, 2002.
27. M.A. Shubin. Pseudodiferential Operators and Spectral Theory, Springer, Berlin, 1987.
28. B. Simon, Trace ideals and their applications, I. London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge. London, New York, Melbourne, 1979.
29. J. Sjöstrand, An algebra of pseudodifferential operators, Math. Res. L. 1 (1994) 185-192.
30. J. Sjöstrand. Wiener type algebras of pseudodifferential operators, Séminaire Equations aux Dérivées Partielles, Ecole Polytechnique, 1994/1995, Exposé No. IV.
31. K. Tachizawa, The boundedness of pseudo-differential operators on modulation spaces, Math. Nachr. 168 (1994) 263-277.
32. J. Toft, Continuity and positivity problems in pseudo-differential calculus. Thesis, Department of Mathematics, University of Lund, Lund, 1996.
33. J. Toft, Regularizations, decompositions and lower bound problems in the Weyl calculus, Comm. Partial Differential Equations 25 (7,8) (2000) 1201-1234.
34. J. Toft, Subalgebras to a Wiener type algebra of pseudo-differential operators, Ann. Inst. Fourier 51 (5) (2001) 1347-1383.
35. J. Toft, Continuity properties for non-commutative convolution algebras with applications in pseudodifferential calculus, Bull. Sci. Math. 126 (2) (2002) 115-142.
36. J. Toft, Modulation spaces and pseudo-differential operators, Research Report, Vol. 2002:05, Blekinge Institute of Technology, Karlskrona, 2002.