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Estimating the diameter of one class of functions in L2
Authors:A A Abilov
Institution:1. V. I. Lenin Dagestan State University, USSR
Abstract:Let
$$\begin{array}{*{20}c} {f(x) \in L_2 - 1,1],||f|| = \sqrt {\int_{ - 1}^1 {|f(x)|^z dx} } } \\ {f_h (x) = \frac{1}{\pi }\int_0^\pi {f(x cos h + \sqrt {1 - x^2 } \sin h cos \pi ) d\theta ,h > 0,} } \\ {\tilde \omega (f^{(r)} ,t) = \mathop {sup}\limits_{0< h< t} ||\sqrt {(1 - x^2 )^r } f^{(r)} (x) - f_h^{(r)} (x)]||,} \\ {\tilde W_\omega ^r = \{ f \in L_2 - 1,1]:\tilde \omega (f^{(r)} ;t) \leqslant c\omega (t)\} ,} \\ \end{array}$$
Keywords:
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