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In this paper, we generalize the continuous quaternion shearlet transform on$\mathbb{R}^{2}$ to $\mathbb{R}^{2d}$, called the multivariate two sidedcontinuous quaternion shearlet transform. Using the two sided quaternionFourier transform, we derive several important properties such as(reconstruction formula, reproducing kernel, plancherel's formula, etc.). Wepresent several example of the multivariate two sided continuous quaternionshearlet transform. We apply the multivariate two sided continuous quaternionshearlet transform properties and the two sided quaternion Fourier transform toestablish Lieb uncertainty principle and the Logarithmic uncertainty principle.Last we study the Beckner's uncertainty principle in term of entropy for themultivariate two sided continuous quaternion shearlet transform.

Lieb, Entropy and Logarithmic uncertainty principles for the multivariate continuous quaternion Shearlet Transform