Boundedness for pseudodifferential operators on multivariate α-modulation spaces

Arkiv for Matematik

Volumn 44, Issue 2, 2006, Pages 241-259

  Borup, Lasse ^a   Nielsen, Morten ^b  

^a AALBORG UNIVERSITY   (Denmark)

^b WASHINGTON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33646556497     PISSN: 00042080     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11512-006-0020-y     Document Type: Article

References (23)

1. BÉNYI, Á. and OKOUDJOU, K., Bilinear pseudodifferential operators on modulation spaces, J. Fourier Anal. Appl. 10 (2004), 301-313.
2. p symbols on modulation spaces, in Advances in Pseudo-Differential Operators, Oper. Theory Adv. Appl. 155, pp. 149-163, Birkhäuser, Basel, 2004.
3. BOGGIATTO, P., BUZANO, E. and RODINO, L., Global Hypoellipticity and Spectral Theory, Mathematical Research 02, Akademie Verlag, Berlin, 1996.
4. BORUP, L., Pseudodifferential operators on α-modulation spaces, J. Funct. Spaces Appl. 2 (2004), 107-123.
5. CÓRDOBA, A. and FEFFERMAN, C., Wave packets and Fourier integral operators, Comm. Partial Differential Equations 3 (1978), 979-1005.
6. FEICHTINGER, H. G., Modulation spaces on locally compact abelian groups, Technical report. University of Vienna, 1983.
7. FEICHTINGER, H. G., Banach spaces of distributions defined by decomposition methods, II, Math. Nachr. 132 (1987), 207-237.
8. FEICHTINGER, H. G. and GRÖBNER, P., Banach spaces of distributions defined by decomposition methods. I, Math. Nachr. 123 (1985), 97-120.
9. GRÖBNER, P., Banachräume glatter Funktionen und Zerlegungsmethoden, Ph.D. thesis, University of Vienna, 1992.
10. GRÖCHENIG, K., Foundations of Time-Frequency Analysis, Applied and Numerical Harmonic Analysis, Birkhäuser, Boston, MA, 2001.
11. GRÖCHENIG, K. and HEIL, C., Modulation spaces and pseudodifferential operators, Integral Equations Operator Theory 34 (1999), 439-457.
12. HÖRMANDER, L., The Analysis of Linear Partial Differential Operators, III, Pseudodifferential Operators, Grundlehren der Mathematischen Wissenschaften 274. Springer, Berlin, 1985.
13. LABATE, D., Pseudodifferential operators on modulation spaces, J. Math. Anal. Appl. 262 (2001), 242-255.
14. NAZARET, B. and HOLSCHNEIDER, M., An interpolation family between Gabor and wavelet transformations: application to differential calculus and construction of anisotropic Banach spaces, in Nonlinear Hyperbolic Equations, Spectral Theory, and Wavelet Transformations, Oper. Theory Adv. Appl. 145, pp. 363-394, Birkhäuser, Basel, 2003.
15. p Math. Nachr. 138 (1988), 145-156.
16. PILIPOVIĆ, S. and TEOFANOV, N., On a symbol class of elliptic pseudodifferential operators, Bull. Cl. Sci. Math. Nat. Sci. Math. 27 (2002), 57-68.
17. PILIPOVIĆ, S. and TEOFANOV, N., Pseudodifferential operators on ultra-modulation spaces, J. Funct. Anal. 208 (2004), 194-228.
18. STEIN, E. M., Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Mathematical Series 43, Princeton University Press, Princeton, NJ, 1993.
19. TACHIZAWA, K., The boundedness of pseudodifferential operators on modulation spaces, Math. Nachr. 168 (1994), 263-277.
20. TOFT, J., Continuity properties for modulation spaces, with applications to pseudodifferential calculus, I, J. Funct. Anal. 207 (2004), 399-429.
21. TOFT, J., Continuity properties for modulation spaces, with applications to pseudodifferential calculus, II, Ann. Global Anal. Geom. 26 (2004), 73-106.
22. TRIEBEL, H., Theory of Function Spaces, Monographs in Mathematics 78, Birkhäuser, Basel, 1983.
23. YAMAZAKI, M., A quasihomogeneous version of paradifferential operators, II, a symbol calculus, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 33 (1986), 311-345.