The sufficient condition of embedding in the Lorentz space

Abstract

In this paper considered the transformation of a series of Fourier-Price in the form k-th difference of the Fourier-Price coefficients. In addition, obtained a sufficient condition the belonging of the function f in a two-parameter Lorentz space in the terms of Fourier-Price coefficients under the conditions that the coefficients of the Fourier-Price the functions f is monotonely, ∆k aν ≥ 0 and a forming sequence of the Price’s system pi, i = 1, 2, ..., is limited, i.e. pi ≤ c, pi ≥ 2, i ∈ N .