Lp boundedness and compactness of localization operators

Localization operators are special anti-Wick operators, which arise in many fields of pure and applied mathematics. We study in this paper some properties of two-wavelet localization operators, i.e., operators which depend on a symbol and two different windows. In the case when the symbol F belongs to Lp(R2n), we give an extension of some results proved by Boggiatto and Wong. More precisely, we obtain the boundedness and compactness of such operators on Lq (Rn), 2p p+1 q 2p p−1, for every p ∈ [1,∞]. © 2005 Elsevier Inc. All rights reserved