Abstract
Daubechies first used localization operators as a mathematical tool to localized a signal in the time frequency plane. They have been a subject of research in many domains ever since. In this paper, we introduce the notion of Weinstein two-wavelet and we define the two-wavelet localization operators in the setting of the Weinstein theory. Then, we give a host of sufficient conditions for the boundedness and compactness of the two-wavelet localization operator on
L
α
p
(
R
+
d
+
1
)
for all
1
≤
p
≤
∞
, in terms of properties of the symbol
σ
and the functions
φ
and
ψ
. In the end, we study some typical examples of the Weinstein two-wavelet localization operators.