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, ∆ _ka_ν ≥ 0 and a forming sequence of the Price’s system p_i,i =1 , 2 ,..., is limited, i.e. p_i ≤ c , p_i ≥2, i ∈ N.