Constructive description of Hölder spaces on a chord-arc curve in ℝ³

Hölder-type function classes with smoothness greater than 1 are introduced on a chord-arc curve in <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-struck upper R cubed"> <mml:semantics> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">R</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msup> <mml:annotation encoding="application/x-tex">\mathbb {R}^3</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. They are characterized constructively in terms of the rate of approximation of functions on the curve by functions harmonic in shrinking neighborhoods of this curve. Commentaries on the definition are also included.