Two-wavelet theory in Weinstein setting

Time-frequency Analysis of two-wavelet theory in Weinstein setting

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 $L^{p}_α(\mathbb{R}^{d+1}_+)$ for all $1\leq p\leq \infty$, 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.