  The aim of this article is to formulate some novel uncertainty principles for
the continuous shearlet transforms in arbitrary space dimensions. Firstly, we
derive an analogue of the Pitt's inequality for the continuous shearlet
transforms, then we formulate the Beckner's uncertainty principle via two
approaches: one based on a sharp estimate from Pitt's inequality and the other
from the classical Beckner's inequality in the Fourier domain. Secondly, we
consider a logarithmic Sobolev inequality for the continuous shearlet
transforms which has a dual relation with Beckner's inequality. Thirdly, we
derive Nazarov's uncertainty principle for the shearlet transforms which shows
that it is impossible for a non-trivial function and its shearlet transform to
be both supported on sets of finite measure. Towards the culmination, we
formulate local uncertainty principles for the continuous shearlet transforms
in arbitrary space dimensions.
