Estimates of analytic functions in Jordan domain

The classical estimates for analytic functions in a disc are carried over to functions which are analytic in Jordan domains whose boundaries are Lipschitz and Radon curves. Singular integrals, maximal estimates, and Lusin's inequality are considered. Analytic functions, the moduli of whose boundary values satisfy the conditions of B. Muckenhoupt are studied in detail. Properties of conformal maps and their level lines connected with the Muckenhoupt conditions on the moduli of the boundary derivatives are considered. This consideration lets one give real proofs of various distortion theorems for conformal maps of Lipschitz domains.