On majorants of $D$-integrable functions

The following majorants are investigated for functions that are integrable in the Denjoy sense: a maximum function in the sense of Hardy and Littlewood; majorants for the conjugate-function operator and for the Hilbert operator. Results of the following kind are obtained:
$$ |\{x\in P:M(x)>\lambda\}|\leqslant\frac C\lambda\biggl((L)\int_P|f|\,dt+\sum_i\omega\biggl(\int f;(a_i,b_i)\biggr)\biggr), $$
where $M$ is the majorant of $f$; $P$ is a closed set with complementary intervals $\{(a_i,b_i)\}$; and $\omega\bigl(\int f;(a_i,b_i)\bigr)$ is the oscillation of an indefinite integral of $f$ on $(a_i,b_i)$.
Bibhography: 9 titles.