In this paper we obtain some estimations of the degree of the best approximation in E1 space of functions by polynomials and rational functions with preas-signed poles, in which D is an Альпер region, its boundary p satisfies the condition ∫0(j(u))/u|lnu|du<∞, where j(u) is the continuous modulus of the angle between the tangent of Γ and the positive real axis as the function of the arc length of Γ. |