An extremum problem on a class of differentiable functions of several variables |
| |
Authors: | D V Gorbachev |
| |
Institution: | 1. Tula State University, Tula, Russia
|
| |
Abstract: | On the multidimensional classW 0 r H ω (n) of continuous periodic functionsF with therth derivativeD r F from $$H_\omega ^{(n)} = \left\{ {f \in C| |f(x) - f(y)| \leqslant \sum\limits_{i = 1}^n {\omega _i } (|x_i - y_i |)\forall x, y \in \mathbb{R}^n } \right\}$$ (where the ω i (x i ) are the convex moduli of continuity) and zero mean with respect to each variable, we obtain the exact value of $$M_r (\omega ) = \mathop {\sup }\limits_{F \in W_0^r H_\omega ^{(n)} } \left\| F \right\|c$$ . |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|