<p>The multivariate shearlet transform (MST) is a novel addition to the class of integral transforms. Knowing the fact that the study of the time-frequency analysis is both theoretically interesting and practically useful, we investigate for this transform some problems of time-frequency analysis. In particular, we study the concept of the linear time-invariant filter associated with the MST. We introduce the generalized Hausdorff type operator in the shearlet domain. We develop nice analysis associated with this operator. In particular, we study the boundedness of this operator and we discuss the properties of its adjoint. The relation between MST and the generalized Hausdorff and its adjoint is established. Next, we extend some uncertainty inequalities for the multivariate shearlet transform. We investigate the Heisenberg uncertainty inequalities for the MST by two approaches, namely the shearlet entropy and the contraction semigroup method. We establish the Donoho–Stark uncertainty principle via the spectral analysis associated with generalized concentration operator. These results are very significant in the field of uncertainty principles. They show that a nonzero signal and its transform can not be both timelimited and bandlimited in the MST domain. We also establish the Faris–Price type uncertainty principle, local uncertainty principles and Benedick–Amrein–Berthier’s uncertainty principle.</p>