On Jackson's inequality for a generalized modulus of continuity in L-2статья
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Аннотация:The value of the sharp constant z in the Jackson type inequality in the space L-2(T-d) En-1(f) less than or equal to komega(psi)(f, T) is studied for the generalized modulus of continuity omega(psi)(f, T) = max(tis an element ofT)(Sigma(s)psi(st)\(f) over cap\(2))(1/2) The value k* of the minimum sharp constant in inequality (1) is found. A class of generalized moduli of continuity is introduced which contains the moduli omega(a,r)(f,delta) := sup(0less than or equal totless than or equal todelta) parallel toDelta(ar-1t)...Delta(at)Delta(t)fparallel to(2), with even a. The relation k = k* is proved in this class for all delta greater than or equal to pi/n.