H{\"o}lder classes in $L^p$ norm on a chord arc curve in $\mathbb R^3$

Abstract

We define H{\"o}lder classes in the $L^p$ norm on a chord-arc curve in $\mathbb{R}^3$ and prove direct and inverse approximation theorems for functions from these classes by functions harmonic in a neighborhood of the curve. The approximation is estimated in the $L^p$ norm, and the smaller the neighborhood, the more accurate the approximation.