ON THE PALEY-WIENER THEOREM FOR A CLASS OF FUNCTIONS OF H~p (0

It is well known that if f(z) belongs to Hardy space H~P in the upper plane, where 1≤p≤∞, then f(x+iy) is the Poisson integral of the corresponding boundary function on real axis. And the Paley-Wiener theorem was proved for 1≤p≤2. The situation becomes different in the ease 0<p<1, since the Poisson integral formula is not established when the boundary value is taken by a function of L~P (0<p<1), which is defined almost everywhere on real axis. The classical argument of the proof of Paley-Wiener theorem does not seem quite appli-