Hardy's Theorem for the (k,2/n)-Fourier Transform

By comparing a function and its (k, 2/n)-Fourier transform to a Gaussian analogue, we establish a Hardy-type uncertainty principle. We extend these results to an Lᵖ-Lq framework, proving a Cowling-Price-type theorem for the (k, 2/n)-Fourier transform. Optimal cases are identified and discussed in detail for both theorems. Furthermore, we investigate the heat equation in this context, deriving a dynamical version of Hardy's theorem that illustrates the temporal evolution of the uncertainty principle in this generalized setting.