On the analysis of anisotropic smoothness

JOURNAL OF APPROXIMATION THEORY

卷:164

Article

Dekel, Shai^1,2 

[1] Tel Aviv Univ, GE Healthcare, IL-69978 Tel Aviv, Israel

[2] Tel Aviv Univ, Sch Math Sci, IL-69978 Tel Aviv, Israel

关键词: Anisotropic function spaces;    Piecewise polynomial approximation;   

DOI  :  10.1016/j.jat.2012.05.002

来源: Elsevier

【 摘 要 】

We investigate anisotropic function spaces defined over the multi-level ellipsoid covers of R-n, where the ellipsoids can quickly change shape from point to point and from level to level. We explicitly define an anisotropic modulus of smoothness (already used implicitly in Dahmen et al. (2010) [4]) and investigate its properties. We show anisotropic variants of classic inequalities such as the Marchaud, Nikolskii and Ul'yanov, relationships with isotropic smoothness and applications to anisotropic Besov space embedding. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free