The special relativistic (space-time) Fourier transform (SFT) in Clifford algebra \(Cl_{(3,1)}\) of space-time, first introduced from a mathematical point of view in Hitzer (Adv Appl Clifford Algebras 17:497–517, 2007), extends the quaternionic Fourier transform to functions, fields and signals in space-time. The purpose of this paper is to advance the study of the SFT and investigate important properties such as continuity, Plancherel identity, Riemann–Lebesgue lemma, and to establish the associated Hausdorff–Young inequality. Moreover, using the observer related space-time split several uncertainty inequalities are established, including Heisenberg’s uncertainty principle and Hardy’s theorem.

时空的Clifford代数\（Cl _ {（3,1）} \）中的特殊相对论（时空）傅里叶变换（SFT），首先是从数学角度从Hitzer（Adv Appl Clifford代数17： 497–517，2007年），将四元傅立叶变换扩展为时空函数，场和信号。本文的目的是推动SFT的研究并研究诸如连续性，Plancherel身份，Riemann-Lebesgue引理等重要属性，并建立相关的Hausdorff-Young不等式。此外，使用与观察者相关的时空分裂，建立了多个不确定性不等式，包括海森堡的不确定性原理和哈迪定理。