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

Vladyslav Babenko; Oleg Kovalenko

paper

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

arXiv:1309.6555

Abstract

Necessary and sufficient conditions on the system of positive numbers $M_{k_{1}}, M_{k_{2}}, M_{k_{3}}, M_{k_{4}}$ , $0 = k_{1} < k_{2} < k_{3} = r - 2$ , $k_{4} = r$ , which guarantee the existence of a function $x \in L_{\infty, \infty}^{r} (R)$ , such that $∥ x^{(k_{i})} ∥_{\infty} = M_{k_{i}}, i = 1, 2, 3, 4,$ are found.

arXiv comment7 pages in English and Russian