The shearlet transform overcomes the limitation of wavelets and Gabor transforms in dealing with image signal, because it has much higher directional sensitivity and provides optimal sparse approximation for 2-D image with curve edge. The author extends Wilczok’s work to continuous shearlet transforms. Two generalizations of the Heisenberg-Pauli-Weyl inequality for \(p\geq 2\) and \(1\leq p\leq 2\) are provided.