Wavelet multipliers on $L^p(\mathbb {R}^n)$
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- by Yu Liu, Alip Mohammed and M. W. Wong PDF
- Proc. Amer. Math. Soc. 136 (2008), 1009-1018 Request permission
Abstract:
We give results on the boundedness and compactness of wavelet multipliers on $L^p(\mathbb {R}^n), 1\leq p\leq \infty$.References
- Colin Bennett and Robert Sharpley, Interpolation of operators, Pure and Applied Mathematics, vol. 129, Academic Press, Inc., Boston, MA, 1988. MR 928802
- Paolo Boggiatto, Alessandro Oliaro, and M. W. Wong, $L^p$ boundedness and compactness of localization operators, J. Math. Anal. Appl. 322 (2006), no. 1, 193–206. MR 2239231, DOI 10.1016/j.jmaa.2005.08.096
- Paolo Boggiatto and M. W. Wong, Two-wavelet localization operators on $L^p(\Bbb R^n)$ for the Weyl-Heisenberg group, Integral Equations Operator Theory 49 (2004), no. 1, 1–10. MR 2057765, DOI 10.1007/s00020-002-1200-1
- Ingrid Daubechies, Time-frequency localization operators: a geometric phase space approach, IEEE Trans. Inform. Theory 34 (1988), no. 4, 605–612. MR 966733, DOI 10.1109/18.9761
- Ingrid Daubechies, Ten lectures on wavelets, CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 61, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1992. MR 1162107, DOI 10.1137/1.9781611970104
- Jingde Du and M. W. Wong, Traces of localization operators, C. R. Math. Acad. Sci. Soc. R. Can. 22 (2000), no. 2, 92–96 (English, with English and French summaries). MR 1764724
- Gerald B. Folland, Introduction to partial differential equations, 2nd ed., Princeton University Press, Princeton, NJ, 1995. MR 1357411
- Zhiping He and M. W. Wong, Localization operators associated to square integrable group representations, PanAmer. Math. J. 6 (1996), no. 1, 93–104. MR 1366611
- Z. He and M. W. Wong, Wavelet multipliers and signals, J. Austral. Math. Soc. Ser. B 40 (1999), no. 4, 437–446. MR 1684253, DOI 10.1017/S0334270000010523
- Bolin Ma and M. W. Wong, $L^p$-boundedness of wavelet multipliers, Hokkaido Math. J. 33 (2004), no. 3, 637–645. MR 2104832, DOI 10.14492/hokmj/1285851914
- M. W. Wong, $L^p$ boundedness of localization operators associated to left regular representations, Proc. Amer. Math. Soc. 130 (2002), no. 10, 2911–2919. MR 1908914, DOI 10.1090/S0002-9939-02-06685-6
- M. W. Wong, Wavelet transforms and localization operators, Operator Theory: Advances and Applications, vol. 136, Birkhäuser Verlag, Basel, 2002. MR 1918652, DOI 10.1007/978-3-0348-8217-0
Additional Information
- Yu Liu
- Affiliation: Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Ontario M3J 1P3, Canada
- Alip Mohammed
- Affiliation: Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Ontario M3J 1P3, Canada
- M. W. Wong
- Affiliation: Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Ontario M3J 1P3, Canada
- Received by editor(s): August 28, 2006
- Received by editor(s) in revised form: December 16, 2006
- Published electronically: November 23, 2007
- Additional Notes: This research was supported by the Natural Sciences and Engineering Research Council of Canada.
- Communicated by: Joseph A. Ball
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 1009-1018
- MSC (2000): Primary 47G10, 47G30
- DOI: https://doi.org/10.1090/S0002-9939-07-09052-1
- MathSciNet review: 2361875