On boundedness of the operator with Cauchy kernel on the real axis

Abstract

Studying boundary value problems and singular integrale quations the class of functions Е (Г) defined on some curve Γ is considered. The main questions that arise in relation to the classes Е (Г) are the following: 1) find the class of functions to which the singular integral (S Гφ) belongs when Е (Г); 2) find the classes of functions that are invariant with respect to the singular integral; 3) find the Banach spaces Е (Г) in which the operator SГ is bounded.