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

Abstract

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 $L_{\alpha }^p({\mathbb{R}}_{+}^{d+1})$ for all $1\le p\le \infty$, in terms of properties of the symbol $\sigma$ and the functions $\phi$ and $\psi$. In the end, we study some typical examples of the Weinstein two-wavelet localization operators.

20 pages. arXiv admin note: text overlap with arXiv:2002.08993

References in corpus (4)

• A variation of the $L^p$ uncertainty principles for the Weinstein transform
• Calderón's reproducing formulas for the Weinstein $L^2$- multiplier operators
• Heisenberg-Pauli-Weyl and Donoho-Stark's uncertainty principle for the Weinstein $L^2$-multiplier operators
• Two-wavelet theory in Weinstein setting