Isometries of some F-algebras of holomorphic functions on the upper half plane

Linear isometries of N ^p (D) onto N ^p (D) are described, where N ^p (D), p > 1, is the set of all holomorphic functions f on the upper half plane D = {z ∈ ?: Im z > 0} such that sup _y >0 ∫_? ln ^p (1 + |(x + iy)|) dx < +∞. Our result is an improvement of the results by D.A. Efimov.