On directional Whitney inequality
| Autor: | Feng Dai, Andriy Prymak |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Modulus of smoothness
General Mathematics 010102 general mathematics Order (ring theory) 41A10 41A25 41A63 52A20 52A40 010103 numerical & computational mathematics Type inequality Numerical Analysis (math.NA) 01 natural sciences Omega Combinatorics Mathematics - Classical Analysis and ODEs Domain (ring theory) Classical Analysis and ODEs (math.CA) FOS: Mathematics Convex body Mathematics - Numerical Analysis 0101 mathematics Mathematics |
| Popis: | This paper studies a new Whitney type inequality on a compact domain $\Omega\subset {\mathbb{R}}^d$ that takes the form $$\inf_{Q\in \Pi_{r-1}^d({\mathcal{E}})} \|f-Q\|_p \leq C(p,r,\Omega) \omega_{{\mathcal{E}}}^r(f,{\rm diam}(\Omega))_p,\ \ r\in {\mathbb{N}},\ \ 00$. It is proved that ${\mathcal{N}}_d(\Omega)=d$ for every connected $C^2$-domain $\Omega\subset {\mathbb{R}}^d$, for $d=2$ and every planar convex body $\Omega\subset {\mathbb{R}}^2$, and for $d\ge 3$ and every almost smooth convex body $\Omega\subset {\mathbb{R}}^d$. [See the pre-print for the complete abstract - not included here due to arXiv limitations.] Comment: the material in this article is based heavily on a part of arXiv:1910.11719 |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|