Lipschitz-Nikolskij constants for the Trotter-Feller operator (Q1917657)

For \(J\subseteq\mathbb{R}\) let \(W^{(q)} (C(J);\alpha;1)\) denote the function class \(\{f\in C^{(q)}(J): |f^{(q)}(x)- f^{(q)}(y)|\leq|x-y|^\alpha\), \(\forall x,y\in J\}\), where \(0<\alpha\leq 1\) and \(q\in\mathbb{N}\cup \{0\}\). The author determines the value of Lipschitz-Nikol'skij constants \(C(\alpha;q;x)\) corresponding to approximations of the function class \(W^{(q)} (C(J);\alpha;1)\) by sequences of operators defined on a domain of functions containing \(W^{(q)} (C(J);\alpha;1)\).