Schatten–von Neumann norms of localization operators. (English) Zbl 1093.47050
This article is a continuation of the author’s work on localization operators [see, e.g., M. W.Wong, “Wavelet transforms and localization operators” (Operator Theory: Advances and Applications 136, Birkhäuser, Basel) (2002; Zbl 1016.42017)] and contains the following two results: firstly, for \(G\) a locally compact group, an exact formula for the Schatten–von Neumann \(p\)-norm (\(1\leq p<\infty\)) of localization operators with symbol in \(L^p(G)\) is given; secondly, for wavelet multipliers with symbol in \(L^p({\mathbb R}^n)\), the Schatten–von Neumann \(p\)-norms are estimated from below.
Reviewer: Oscar Bandtlow (London)
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 |
| 22D10 | Unitary representations of locally compact groups |
