Schatten–von Neumann norm inequalities for two-wavelet localization operators. (English) Zbl 1143.47032
Rodino, Luigi (ed.) et al., Pseudo-differential operators. Partial differential equations and time-frequency analysis. Selected papers of the ISAAC workshop, Toronto, Canada, December 11–15, 2006. Providence, RI: American Mathematical Society (AMS); Toronto: The Fields Institute for Research in Mathematical Sciences (ISBN 978-0-8218-4276-8/hbk). Fields Institute Communications 52, 265-277 (2007).
The paper is an extension of results of [M.-W.Wong, “Wavelet transforms and localization operators”, Basel:Birkhäuser (2002; Zbl 1016.42017)] concerning the Hilbert-Schmidt norm for one-wavelet localization operators to similar results for two-wavelet localization operators. It is shown that every two-wavelet localization operator whose symbol is in \(L^p(G)\) is in the Schatten-von Neumann class \(S_p\) for \(1\leq p \leq \infty\). An upper bound and a lower bound of the Hilbert-Schmidt norm are given for two-wavelet localization operators without using interpolation theory.
For the entire collection see [Zbl 1126.35007].
For the entire collection see [Zbl 1126.35007].
Reviewer: Mohammad Sal Moslehian (Mashhad)
MSC:
| 47G10 | Integral operators |
| 47B10 | Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.) |
| 42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
