2017
Том 69
№ 6

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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.

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Abstract

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 $||x^{(k_i)} ||_{\infty} = M_{k_i},\quad i = 1, 2, 3, 4$.

English version (Springer): Ukrainian Mathematical Journal 64 (2012), no. 5, pp 672-679.

Citation Example: Babenko V. F., Kovalenko O. V. On the dependence of the norm of a function on the norms of its derivatives of orders $k$ , $r - 2$ and $r , 0 < k < r - 2$ // Ukr. Mat. Zh. - 2012. - 64, № 5. - pp. 597-603.

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