Schatten-von Neumann properties for Fourier integral operators with non-smooth symbols, I

Arkiv for Matematik

Volumn 47, Issue 2, 2009, Pages 295-312

  Concetti, Francesco ^a   Toft, Joachim ^b  

^a UNIVERSITY OF TURIN   (Italy)

^b LINNAEUS UNIVERSITY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 70350169458     PISSN: 00042080     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11512-008-0075-z     Document Type: Article

References (26)

1. n), Japan. J. Math.4 (1978), 299-361.
2. Baoxiang, W. and Chunyan, H., Frequency-uniform decomposition method for the generalized BO, KdV and NLS equations, J. Differential Equations239 (2007), 213-250.
3. Bergh, J. and Löfström, J., Interpolation Spaces, Grundlehren der Mathematischen Wissenschaften 223, Springer, Berlin-Heidelberg, 1976.
4. Birman, M. Sh. and Solomyak, M. Z., Estimates of singular numbers of integral operators, Uspekhi Mat. Nauk 32:1 (1977), 17-84, 271 (Russian) English transl.: Russian Math. Surveys32:1 (1977), 15-89.
5. Boulkhemair, A., Remarks on a Wiener type pseudodifferential algebra and Fourier integral operators, Math. Res. Lett.4 (1997), 53-67.
6. Feichtinger, H. G., Banach spaces of distributions of Wiener's type and interpolation, in Functional Analysis and Approximation (Oberwolfach, 1980), Internat. Ser. Numer. Math. 60, pp. 153-165, Birkhäuser, Basel, 1981.
7. Feichtinger, H. G., Banach convolution algebras of Wiener type, in Functions, Series, Operators, Vol. I, II (Budapest, 1980), Colloq. Math. Soc. János Bolyai 35, pp. 509-524, North-Holland, Amsterdam, 1983.
8. Feichtinger, H. G., Atomic characterizations of modulation spaces through Gabor-type representations, Rocky Mountain J. Math.19 (1989), 113-125.
9. Feichtinger, H. G., Modulation spaces on locally compact abelian groups, in Wavelets and their Applications, pp. 99-140, Allied Publishers Private Limited, New Delhi, 2003.
10. Feichtinger, H. G. and Gröchenig, K. H., Banach spaces related to integrable group representations and their atomic decompositions. I, J. Funct. Anal.86 (1989), 307-340.
11. Feichtinger, H. G. and Gröchenig, K. H., Banach spaces related to integrable group representations and their atomic decompositions. II, Monatsh. Math.108 (1989), 129-148.
12. Feichtinger, H. G. and Gröchenig, K. H., Gabor frames and time-frequency analysis of distributions, J. Funct. Anal.146 (1997), 464-495.
13. Gröchenig, K., Foundations of Time-Frequency Analysis, Appl. Numer. Harmon. Anal., Birkhäuser, Boston, MA, 2001.
14. Gröchenig, K. and Heil, C., Modulation spaces and pseudodifferential operators, Integral Equations Operator Theory34 (1999), 439-457.
15. Hörmander, L., The Analysis of Linear Partial Differential Operators. I, III, Grundlehren der Mathematischen Wissenschaften 256, 274, Springer, Berlin-Heidelberg, 1983, 1985.
16. Pilipović, S. and Teofanov, N., Wilson bases and ultramodulation spaces, Math. Nachr.242 (2002), 179-196.
17. 2 for a class of Fourier integral operators with symbols in Besov spaces, Uspekhi Mat. Nauk 58:5 (2003), 201-202 (Russian). English transl.: Russian Math. Surveys 58 (2003), 1044-1046.
18. 2-boundedness theorems for a class of Fourier integral operators, Comm. Partial Differential Equations31 (2006), 547-569.
19. Ruzhansky, M. and Sugimoto, M., A smoothing property of Schrödinger equations in the critical case, Math. Ann.335 (2006), 645-673.
20. Simon, B., Trace Ideals and their Applications, London Mathematical Society Lecture Note Series 35, Cambridge University Press, Cambridge, 1979.
21. Sjöstrand, J., An algebra of pseudodifferential operators, Math. Res. Lett.1 (1994), 185-192.
22. Sugimoto, M. and Tomita, N., The dilation property of modulation spaces and their inclusion relation with Besov spaces, J. Funct. Anal.248 (2007), 79-106.
23. Teofanov, N., Ultramodulation Spaces and Pseudodifferential Operators, Endowment Andrejević, Belgrade, 2003.
24. Toft, J., Continuity and Positivity Problems in Pseudo-Differential Calculus. Ph.D. Thesis, University of Lund, Lund, 1996.
25. Toft, J., Subalgebras to a Wiener type algebra of pseudo-differential operators, Ann. Inst. Fourier (Grenoble)51:5 (2001), 1347-1383.
26. Toft, J., Continuity properties for modulation spaces, with applications to pseudo-differential calculus. I, J. Funct. Anal.207 (2004), 399-429.