This paper deals with the study of some uncertainty principles associated with the directional short-time Fourier transform. First, we develop the Beckner’s uncertainty principle by invoking the well-known Pitt’s inequality and then study some logarithmic Sobolev-type inequalities. Second, we present a couple of concentration uncertainty principles, including the Benedick–Amrein–Berthier inequality and the local-type uncertainty principle. We culminate our study by formulating the Donoho–Stark-type uncertainty principles for the directional short-time Fourier transform.

中文翻译：

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与定向短时傅立叶变换相关的不确定性原理

本文涉及与定向短时傅立叶变换相关的一些不确定性原理的研究。首先，我们通过调用众所周知的皮特不等式来发展贝克纳不确定性原理，然后研究一些对数 Sobolev 型不等式。其次，我们提出了几个浓度不确定性原理，包括 Benedick-Amrein-Berthier 不等式和局部类型不确定性原理。我们通过为定向短时傅立叶变换制定 Donoho-Stark 型不确定性原理来结束我们的研究。