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Оценка нормы функции, ортогональной кусочно-постоянным, через второй модуль непрерывности.

Ихсанов Л. Н.

The article is concerned with the question about the constant
$$
W_2^*=\sup_{f\in F^0}\frac{\|f\|}{\omega_2(f,\,1)},
$$
there $F^0$ stands for the space of bounded functions $f$ with the property
$$
\int\limits_k^{k+1}f(x)\,dx=0\quad\forall k\in\mathbb{Z}.
$$

The suggested approach allowed to narrow down the known range for the desired constant
as well as the set of functions it could be obtained on.

It is shown that $W_2^*$ also happens to be the exact constant in a related Jackson--Stechkin type inequality.