Constructive description of H{\"o}lder-like classes on an arc in $\mathbb{R}^3$ by means of harmonic functions

TL;DR

This paper provides a constructive method to describe Hölder-like function classes on curves in three-dimensional space using harmonic functions, linking approximation rates to function regularity.

Contribution

It introduces a new constructive characterization of Hölder-like classes on curves in bcs3 using harmonic function approximation in shrinking neighborhoods.

Findings

Provides a constructive description of Hölder-like classes on curves in bcs3.

Establishes a link between approximation rates by harmonic functions and function regularity.

Offers a new approach to analyze function classes on curves in three-dimensional space.

Abstract

We give a constructive description of H{\"o}lder-like classes of functions on chord-arc curves in $\mathbb{R}^3$ in terms of a rate of approximation by harmonic functions in shrinking neighborhoods of those curve.