Complete moment convergence for the discrete Fourier transform of random fields

For a field { 𝑋 𝐧 , 𝐧 ∈ ℤ 𝑑 + } of random variables, by establishing some general moment inequalities, some results on the complete moment convergence for the discrete Fourier transform ∑ 𝐤 ⪯ 𝐧 𝑒 𝑖 ⁢ 𝐤 ⋅ 𝐭 ⁢ 𝑋 𝐤 of random fields are obtained. The results improve the corresponding ones in the literature. Furthermore, we investigate some new case that was not addressed in the existing literature.