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Applicable Analysis
An International Journal
Volume 84, 2005 - Issue 3
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Original Articles

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

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Pages 269-282 | Received 02 Jan 2003, Accepted 01 Apr 2003, Published online: 17 Aug 2006

References

  • Boggiatto P 2004 Localization Operators with Lp 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
  • Boggiatto P 2003 Localization Operators with Lp Symbols on Modulation Spaces preprint Quaderni Dip. Mat. Univ. Torino, n. 7
  • 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
  • Boggiatto , P , Buzano , E and Rodino , L . 1996 . Global Hypoellipticity and Spectral Theory . Journal of Functional Analysis , 205 : 107 – 131 .
  • Cordero , E and Gröchenig , K . 2002 . Time-frequency analysis of localization operators . Journal of Functional Analysis , 205 ( 1 ) : 107 – 131 .
  • Dörfler , M , Gröchenig , K and Feichtinger , H . 2002 . Compactness criteria in function spaces . Collectanea Mathematica , 94 ( 1 )
  • Feichtinger H 1983 Modulation Spaces on Locally Compact Abelian Groups Technical report, University of Vienna, Vienna
  • 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 .
  • Feichtinger , HG and Gröchenig , KH . 1989 . Banach spaces related to integrable group representations and their atomic decompositions, II . Monatshefte fur Mathematik , 108 : 129 – 148 .
  • Folland GB 1989 Harmonic Analysis in Phase Space Princeton Princeton U.P.
  • Gröchenig K 2001 Foundations of Time-Frequency Analysis Boston Birkhäuser
  • 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 .
  • He , Z and Wong , MW . 1996 . Localization operators associated to square integrable group representations . Panamerican Mathematical Journal , 6 ( 1 ) : 93 – 104 .
  • Hörmander L 1983, 1985 The Analysis of Linear Partial Differential Operators Berlin, Heidelberg, New York, Tokyo Springer-Verlag
  • Lieb , EH . 1990 . Integral bounds for radar ambiguity functions and Wigner distributions . Journal of Mathematical Physics , 31 : 594 – 599 .
  • Shubin MA 2001 Pseudodifferential Operators and Spectral Theory Berlin Springer-Verlag
  • Simon B 1979 Trace ideals and their applications London Mathematical Society Lecture Note Series Cambridge, London, New York, Melbourne Cambridge University Press
  • Toft , J . 2002 . Continuity properties for non-commutative convolution algebras with applications in pseudo-differential calculus . Bulletin des Sciences Mathematiques , 126 ( 2 ) : 115 – 142 .
  • Toft J 2002 Modulation Spaces and Pseudo-differential Operators Research Report, Vol. 2002:05 Blekinge Institute of Technology Karlskrona
  • Toft , J . 2004 . Continuity properties for modulation spaces with applications in pseudo-differential calculus I . Journal of Functional Analysis , 207 ( 2 ) : 399 – 429 .
  • 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 .
  • Toft J 2003 Modulation Spaces of Non-standard Type and Pseudo-differential Operators Research Report, Vol. 2003:01 Blekinge Institute of Technology Karlskrona
  • Wong MW 1998 Weyl Transforms New York Springer-Verlag
  • 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)
  • Wong MW 2002 Wavelet Transform and Localization Operators Boston Birkhäuser

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