2018
Том 70
№ 11

All Issues

Kovalenko O. V.

Articles: 2
Article (Ukrainian)

On the dependence of the norm of a multiply monotone function on the norms of its derivatives

Bondarenko A. R., Kovalenko O. V.

↓ Abstract

Ukr. Mat. Zh. - 2018. - 70, № 7. - pp. 867-875

We establish necessary and sufficient conditions for a system of positive numbers Mk1 , Mk2 , Mk3 , Mk4 , 0 = k1 < < k2 < k3 \leq r 3, k4 = r guaranteeing the existence of an (r 2)-monotone function x on the half line such that \| x(ki)\| \infty = Mki , i = 1, 2, 3, 4.

Article (Russian)

On the dependence of the norm of a function on the norms of its derivatives of orders $k$ , $r - 2$ and $r , 0 < k < r - 2$

Babenko V. F., Kovalenko O. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2012. - 64, № 5. - pp. 597-603

We establish conditions for a system of positive numbers $M_{k_1}, M_{k_2}, M_{k_3}, M_{k_4}, \; 0 = k_1 < k2 < k3 = r − 2, k4 = r$, necessary and sufficient for the existence of a function $x \in L^r_{\infty, \infty}(R)$ such that $||x^{(k_i)} ||_{\infty} = M_{k_i},\quad i = 1, 2, 3, 4$.