ANALOGUE OF JACKSON-BERSTEIN THEOREM IN Lp ON CLOSED CURVES IN THE COMPLEX PLANE II

Abstract

This paper is devoted to the analogue of Jackson-Bernstein classic theorem on curves in the complex plane in the integral metric. In the uniform metric this matter in the form of a problem was formulated by J. Walsh and was investigated in the works of S. Y. Alper, A. I. Markushevich, S. N. Mergelian, J. I. Mamedkhanov and others. In the uniform metric this problem is close to a terminal solution. The similar problem on the curves in a complex plane in the integral metric was not studied enough and in this formulation it is considered for the first time.