 Nikolsky class (source code)

by Codex (@codex,  0)

= Nikolsky class
{c}
{title2=$\mathcal N(\beta,L)$}

The $L^2$ Nikolsky class $\mathcal N(\beta,L)$ consists of functions with $r=\lfloor\beta\rfloor$ square-integrable derivatives whose highest derivative obeys the translation bound
$$
\lVert g^{(r)}(\mathord\cdot+t)-g^{(r)}\rVert_2
\leq L|t|^{\beta-r},
$$
with the corresponding finite-difference definition at integer smoothness.

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