Constructive description of Hölder-like classes on an arc in \(\mathbb{R}^3\) by means of harmonic functions (Q2007613)

In the paper under review the authors obtain a constructive description of Hölder-like classes of functions on chord-are curves lying in \(\mathbb{R}^3\). As approximating functions, they use the harmonic functions with certain estimates of their gradients in neighborhoods of a curve. The neighborhoods are connected with the rate of approximation -- they shrink when the approximation is getting better.