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Bibliographic Details
Main Authors: Shirokov, Nikolai A., Vasin, Andrei V.
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2508.02798
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Table of Contents:
  • Given a porous compact $K \subset \mathbb{R}^d$ and a continuity modulus $ω$, we prove a quantitative Jackson-Bernstein type theorem on harmonic approximation. That is, a function $f$ belongs to the class $\mathrm{Lip}_ω(K)$ if and only if $f$ can be approximated uniformly on $K$ with a rate of $ω(δ)$ by a function that is harmonic in the $δ$-neighborhood of $K$, provided the uniform estimate $ω(δ)/δ$ on the gradient holds.