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.

中文翻译：

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任意空间维度连续剪切波变换的不确定性原理

摘要 本文的目的是为任意空间维度中的连续剪切波变换制定一些新的不确定性原理。首先，我们推导出连续剪切波变换的皮特不等式的类似物，然后我们通过两种方法来制定贝克纳不确定性原理：一种基于皮特不等式的尖锐估计，另一种基于傅立叶域中的经典贝克纳不等式。继续，获得与贝克纳不等式具有双重关系的对数 Sobolev 不等式的一个版本。随后，还推导出了任意空间维度中连续剪切波变换的 Nazarov 不确定性原理。