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

TL;DR

This paper provides a constructive method to describe H"older-like function classes on a chord-arc curve in three-dimensional space using harmonic approximation within shrinking neighborhoods.

Contribution

It introduces a new constructive characterization of H"older-like classes on curves in bcsbcrb3 using harmonic functions and approximation rates.

Findings

Provides a constructive description of Hb6lder-like classes on curves in bcsbcrb3

Uses harmonic approximation in shrinking neighborhoods

Establishes a rate of approximation for these classes

Abstract

We give a constructive description of H\"older-like classes of functions on a chord-arc curve in $\mathbb{R}^3$ by means of a rate of approximation by function harmonic is shrinking neibourhoods of those curve