On the interpolation between certain theorems on Fourier transforms

It is well known that if f(x) belongs to L^P(R), 1 < P ≤ 2, then the Hausdorff-Young inequality ([1],

Theorem 74) asserts that its Fourier transform f(u) belongs to L^P1 (R), where

1/P¹ +1/P = 1