ON INTEGRALS OF CONJUGATE FUNCTIONS

Abstract

This paper is devoted to problems of integrability of conjugate functions. We study the problem of when the validity of the Riesz equation for a single function implies its validity for other functions, and also the problems of the integrability in the Denjoy-Hincin sense of functions conjugate to summable functions, of the integrability in the Lebesgue sense of functions conjugate to Denjoy-Hincin integrable functions, and of the A-, A*- and U-integrability of functions conjugate to functions that have improper Lebesgue integrals. Bibliography: 15 titles.