Embeddings of some classical banach spaces into modulation spaces

Proceedings of the American Mathematical Society

Volumn 132, Issue 6, 2004, Pages 1639-1647

  Okoudjou, Kasso A ^a,b  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^b Department of Obstetrics Gynecology   (United States)

Author keywords

Besov space; Modulation space; Short time Fourier transform; Sobolev space; Time frequency analysis; Triebel Lizorkin space

Indexed keywords

EID: 2442713801     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9939-04-07401-5     Document Type: Conference Paper

References (16)

1. H. G. Feichtinger, Modulation spaces on locally Abelian groups, Technical Report, University of Vienna, 1983.
2. H. G. Feichtinger and K. Gröchenig, Banach spaces related to integrable group representations and their atomic decompositions. I, J. Funct. Anal. 86:307-340, 1989. MR 91g:43011
3. H. G. Feichtinger and K. Gröchenig, Banach spaces related to integrable group representations and their atomic decompositions. II, Monatsh. Math. 108:129-148, 1989. MR 91g:43012
4. G. B. Folland, Harmonic Analysis in Phase Space, Annals of Mathematics Studies, vol. 122, Princeton University Press, Princeton, NJ, 1989. MR 92k:22017
5. Y. V. Galperin and K. Gröchenig, Uncertainty principles as embeddings of modulation spaces, J. Math. Anal. Appl. 274(1):181-202, 2002. MR 2003h:46040
6. P. Gröbner, Banachräume Glatter Funktionen und Zerlegungsmethoden, Ph.D. Thesis, University of Vienna, 1983.
7. K. Gröchenig, An uncertainty principle related to the Poisson summation formula, Studia Math. 121:87-104, 1996. MR 98a:42007
8. K. Gröchenig, Foundations of Time-Frequency Analysis, Applied and Numerical Harmonic Analysis, Birkhäuser, Boston, MA, 2001. MR 2002h:42001
9. K. Gröchenig and C. Heil, Modulation spaces and pseudodifferential operators, Integral Equations Operator Theory 34:439-457, 1999. MR 2001a:47051
10. C. Heil, J. Ramanathan, and P. Topiwala, Singular values of compact pseudodifferential operators, J. Funct. Anal. 150:426-452, 1997. MR 98k:47102
11. J. A. Hogan and J. D. Lakey, Embeddings and uncertainty principles for generalized modulation spaces, in "Sampling Theory and Its Applications," J. J. Benedetto and P. Ferreira, eds., Modern Sampling Theory - Mathematics and Applications, Birkhäuser, Boston, MA, 2001. MR 2003a:94003
12. T. Runst and W. Sickel, Sobolev Spaces of Fractional Order, Nemytskij Operators, and Non-linear Partial Differential Equations, Walter de Gruyter, Berlin, 1996. MR 98a:47071
13. E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, NJ, 1970. MR 44:7280
14. J. Toft, Embeddings for modulation spaces and Besov spaces, Research Report 2001:11, Blekinge Institute of Technology, 2002.
15. H. Triebel, Theory of Function Spaces, Monographs in Mathematics, No. 78, Birkhäuser Verlag, Basel, 1983. MR 86j:46026
16. H. Triebel, Theory of Function Spaces II, Monographs in Mathematics, No. 84, Birkhäuser Verlag, Basel, 1992. MR 93f:46029