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

  • V. F. Babenko
  • O. V. Kovalenko Днепропетр. нац. ун-т

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 $||x^{(k_i)} ||_{\infty} = M_{k_i},\quad i = 1, 2, 3, 4$.
Published
25.05.2012
How to Cite
BabenkoV. F., and KovalenkoO. V. “On the Dependence of the Norm of a Function on the Norms of Its Derivatives of Orders $k$ , $r - 2$ and $r , 0 < K &lt; R - 2$”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, no. 5, May 2012, pp. 597-03, http://umj.imath.kiev.ua/index.php/umj/article/view/2600.
Section
Research articles