A class of Fourier multipliers for modulation spaces

Applied and Computational Harmonic Analysis

Volumn 19, Issue 1, 2005, Pages 131-139

  Bényi, Árpád ^a   Grafakos, Loukas ^b   Gröchenig, Karlheinz ^c   Okoudjou, Kasso ^d  

^a UNIVERSITY OF MASSACHUSETTS   (United States)

^b UNIVERSITY OF MISSOURI   (United States)

^c INSTITUTE OF EPIDEMIOLOGY   (Germany)

^d Department of Obstetrics Gynecology   (United States)

Author keywords

Fourier multipliers; Gabor frames; Hilbert transform; Modulation spaces; Short time Fourier transform

Indexed keywords

FOURIER TRANSFORMS; FUNCTIONS; INTERPOLATION; MATHEMATICAL OPERATORS; NUMBER THEORY; SET THEORY;

FOURIER MULTIPLIERS; GABOR FRAMES; HILBERT TRANSFORM; MODULATION SPACES; SHORT-TIME FOURIER TRANSFORM;

MODULATION;

EID: 20144385878     PISSN: 10635203     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.acha.2005.02.002     Document Type: Letter

References (25)

1. I. Daubechies Ten Lectures on Wavelets 1992 SIAM Philadelphia, PA
2. J. Duandikoetxea Fourier Analysis Graduate Studies in Mathematics vol. 29 2001 American Mathematical Society Providence, RI
3. H.G. Feichtinger On a new Segal algebra Monatsh. Math. 92 1981 269 289
4. H.G. Feichtinger, Modulation spaces on locally Abelian groups, Technical Report, University of Vienna, 1983
5. updated version appeared in Proceedings of International Conference on Wavelets and Applications, Chennai, India, 2003, pp. 99-140
6. H.G. Feichtinger, and K. Gröchenig Banach spaces related to integrable group representations and their atomic decompositions I J. Funct. Anal. 86 1989 307 334
7. H.G. Feichtinger, and K. Gröchenig Banach spaces related to integrable group representations and their atomic decompositions II Monatsh. Math. 108 1989 129 148
8. G.B. Folland Harmonic Analysis in Phase Space Ann. of Math. Studies 1989 Princeton Univ. Press Princeton, NJ
9. E. Galperin, and K. Gröchenig Uncertainty principles as embeddings of modulation spaces J. Math. Anal. Appl. 271 2002 181 202
10. L. Grafakos Classical and Modern Fourier Analysis 2003 Prentice Hall Upper Saddle River, NJ
11. K. Gröchenig Foundations of Time-Frequency Analysis 2001 Birkhäuser Boston, MA
12. K. Gröchenig, and C. Heil Modulation spaces and pseudodifferential operators Integral Equations Operator Theory 34 1999 439 457
13. K. Gröchenig, and C. Heil Counterexamples for boundedness of pseudodifferential operators Osaka J. Math. 41 2004 1 11
14. G.H. Hardy, J.E. Littlewood, and G. Pólya Inequalities 1952 Cambridge Univ. Press Cambridge
15. C. Heil Integral operators, pseudodifferential operators, and Gabor frames H.G. Feichtinger T. Strohmer Advances in Gabor Analysis 2003 Birkhäuser Boston, MA 153 169
16. C. Heil, J. Ramanathan, and P. Topiwala Singular values of compact pseudodifferential operators J. Funct. Anal. 150 1997 426 452
17. C. Heil, and D. Walnut Continuous and discrete wavelet transforms SIAM Rev. 31 1989 628 666
18. J.A. Hogan, and J.D. Lakey Embeddings and uncertainty principles for generalized modulation spaces J.J. Benedetto P.J.S.G. Ferreira Modern Sampling Theory 2001 Birkhäuser Boston, MA 73 105
19. D. Labate Time-frequency analysis of pseudodifferential operators Monatsh. Math. 133 2001 143 156
20. D. Labate Pseudodifferential operators on modulation spaces J. Math. Anal. Appl. 262 2001 242 255
21. K.A. Okoudjou, Characterization of function spaces and boundedness of bilinear pseudodifferential operators through Gabor frames, Ph.D. thesis, Georgia Institute of Technology, Atlanta, 2003
22. M. Riesz Sur les fonctions conjuguées Math. Z. 27 1928 218 244
23. E.C. Titchmarsh An inequality in the theory of series J. London Math. Soc. 3 1928 81 83
24. J. Toft Modulation spaces and pseudodifferential operators I J. Funct. Anal. 207 2004 399 429
25. 0(G) Canad. J. Math. 39 1 1987 123 148