ON PROPERTIES OF FUNCTIONS OF BOUNDED VARIATION ON A SET

The Kolmogorov inequality for conjugate functions is generalized in ?1. Theorem?2 is the main result; it shows, for example, that if a function is -periodic to within linearity and of bounded variation in the narrow sense on a set , then for any 0$ SRC=http://ej.iop.org/images/0025-5734/50/1/A04/tex_sm_2732_img4.gif/> In ?2 a well-known theorem of F. and M.?Riesz is generalized. In particular, the following is proved.Theorem 5. Suppose that a -periodic integrable function and its conjugate are defined everywhere, bounded, and of bounded variation in the narrow sense on a set , and that if and exist at a point . Then and are absolutely continuous in the narrow sense on .Bibliography: 14 titles.