Constructive Characterization of Analogue of Lipschitz Class in Integral Metric

We introduced the basic classes of curves (1) on which approximation is conducted and obtained constructive characteristic of analogue of Lipschitz class on curves in a complex plane in integral metrics. For that we proved an inverse theorem and to get a constructive characteristic for the analogue of Lipschitz class of order α on the curves (1) in a complex plane in the metric Lp(Γ), i.e. for the class Hpa(Γ) (P > 1) and 0 < α < 1.. The obtained result is a solution the analogue of J.L. Walsh problem related to Jackson-Bernstein classic theorem.