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

Abstract

We define H{ö}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.

18 pages