On Benedicks-Amrein-Berthier uncertainty principles for continuous quaternion wavelet transform

The continuous quaternion wavelet transform (CQWT) can refine a quaternion function in the multiscale framework by stretching and translation to achieve an effect of the localized analysis. In this paper, we are devoted to some different types of uncertainty principles (UPs) for the two-dimensional CQWT. More precisely, we obtain the Benedicks-Amrein-Berthier UP and the logarithmic Sobolev-type UP for the CQWT. As a direct consequence, we also deduce some significant corollaries, such as the Benedicks UP, the general Heisenberg-type UP, the general concentration UP, and the concentration logarithmic Sobolev-type UP for the CQWT.