Asymptotic behavior of the two-point Wightman function

It is shown that there is a one-to-one correspondence between the quasiasymptotic behavior of the two-point Wightman function in the $p$ representation and the asymptotic behavior of the Fourier transform in the neighborhood of the light cone. As a consequence, the modified Tauber theorem of Vladimirov is used to obtain an assertion about the connection between the asymptotic behavior of the antiderivative of the two-point function at infinity and the behavior of the Laplace transform in the neighborhood of the origin.