The discussion focuses on proving that the function f(x) = (1 + |x|)^{-a} is the Fourier transform of an integrable function on R when a > 1, with the condition for convergence of the inverse transform being that the denominator must have a power greater than 1. When 0 < a <= 1, the function fails to meet this condition, indicating it is not integrable. The function f(x) = 1/(log(|x|^2 + 2)) is also questioned regarding its integrability and Fourier transform properties. Participants express uncertainty about formalizing their arguments and seek assistance with the concepts. The conversation emphasizes the importance of understanding integrability conditions in Fourier transforms.