Uncertainty principles for the continuous shearlet transforms in arbitrary space dimensions

Abstract

ABSTRACT The aim of this article is to formulate some new uncertainty principles for the continuous shearlet transforms in arbitrary space dimensions. Firstly, we derive an analogue of Pitt's inequality for the continuous shearlet transforms, then we formulate Beckner's uncertainty principle via two approaches: one based on a sharp estimate from Pitt's inequality and the other from the classical Beckner inequality in the Fourier domain. In continuation, a version of the logarithmic Sobolev inequality having a dual relation with Beckner's inequality is obtained. In sequel, the Nazarov's uncertainty principle is also derived for the continuous shearlet transforms in arbitrary space dimensions. The article concludes with the formulation of certain new local type uncertainty principles for the continuous shearlet transforms in arbitrary space dimensions.