Embeddings and compactness for generalized Sobolev–Shubin spaces and modulation spaces

International Journal of Phytoremediation

Volumn 84, Issue 3, 2005, Pages 269-282

  Boggiatto, Paolo ^a   Toft, Joachim ^b  

^a UNIVERSITY OF TURIN   (Italy)

^b BLEKINGE INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

46B50; 46E35; 47B35; 47L80; Compactness; Localization operators; Modulation spaces; MSC: primary 42B35; Secondary 54D30; Shubin; Sobolev; Toeplitz operators

Indexed keywords

EID: 33646596646     PISSN: 15226514     EISSN: 15497879     Source Type: Journal    
DOI: 10.1080/00036810412331297253     Document Type: Article

References (25)

1. p symbols on modulation spaces In: P. Boggiatto, R. Ashino and M.W. Wong (Eds.) Advances in Pseudo-Differential Operators, Operator Theory:Advances and Applications pp. 149–164 Basel Birkhäuser Verlag
2. p Symbols on Modulation Spaces preprint Quaderni Dip. Mat. Univ. Torino, n. 7
3. Boggiatto P, Cordero E, Gröchenig K, 2002 Generalized Anti-Wick Operators with Symbols in Distributional Sobolev spaces Research Report, Quaderni Dip. Mat. Univ. Torino, n. 32
4. Boggiatto, P, Buzano, E, and Rodino, L. 1996. Global Hypoellipticity and Spectral Theory. Journal of Functional Analysis, 205: 107–131.
5. Cordero, E, and Gröchenig, K. 2002. Time-frequency analysis of localization operators. Journal of Functional Analysis, 205 (1): 107–131.
6. Dörfler, M, Gröchenig, K, and Feichtinger, H. 2002. Compactness criteria in function spaces. Collectanea Mathematica, 94 (1)
7. Feichtinger H, 1983 Modulation Spaces on Locally Compact Abelian Groups Technical report, University of Vienna, Vienna
8. Feichtinger, HG, and Gröchenig, KH. 1989. Banach spaces related to integrable group representations and their atomic decompositions, I. Journal of Functional Analysis, 86: 307–340.
9. Feichtinger, HG, and Gröchenig, KH. 1989. Banach spaces related to integrable group representations and their atomic decompositions, II. Monatshefte fur Mathematik, 108: 129–148.
10. Folland GB, 1989 Harmonic Analysis in Phase Space Princeton Princeton U.P.
11. Gröchenig K, 2001 Foundations of Time-Frequency Analysis Boston Birkhäuser
12. Grossmann, A, Loupias, G, and Stein, EM. 1968. An algebra of pseudo-differential operators and quantum mechanics in phase space. Annales de l'Institut Fourier, 18: 343–368.
13. He, Z, and Wong, MW. 1996. Localization operators associated to square integrable group representations. Panamerican Mathematical Journal, 6 (1): 93–104.
14. Hörmander L, 1983, 1985 The Analysis of Linear Partial Differential Operators Berlin, Heidelberg, New York, Tokyo Springer-Verlag
15. Lieb, EH. 1990. Integral bounds for radar ambiguity functions and Wigner distributions. Journal of Mathematical Physics, 31: 594–599.
16. Shubin MA, 2001 Pseudodifferential Operators and Spectral Theory Berlin Springer-Verlag
17. Simon B, 1979 Trace ideals and their applications London Mathematical Society Lecture Note Series Cambridge, London, New York, Melbourne Cambridge University Press
18. Toft, J. 2002. Continuity properties for non-commutative convolution algebras with applications in pseudo-differential calculus. Bulletin des Sciences Mathematiques, 126 (2): 115–142.
19. Toft J, 2002 Modulation Spaces and Pseudo-differential Operators Research Report, Vol. 2002:05 Blekinge Institute of Technology Karlskrona
20. Toft, J. 2004. Continuity properties for modulation spaces with applications in pseudo-differential calculus I. Journal of Functional Analysis, 207 (2): 399–429.
21. Toft, J. 2004. Continuity properties for modulation spaces with applications in pseudo-differential calculus II. Annals of Global Analysis and Geometry, 26 (1): 73–106.
22. Toft J, 2003 Modulation Spaces of Non-standard Type and Pseudo-differential Operators Research Report, Vol. 2003:01 Blekinge Institute of Technology Karlskrona
23. Wong MW, 1998 Weyl Transforms New York Springer-Verlag
24. Wong MW, 2001 In: R.S. Pathak (Ed.) Localization Operators on the Weyl-Heisenberg Group, in Geometry, Analysis and Applications pp. 303–314 (World Scientific)
25. Wong MW, 2002 Wavelet Transform and Localization Operators Boston Birkhäuser