Ditzian, Z.; Prymak, A. Extension technique and estimates for moduli of smoothness on domains in \(\mathbb{R}^d\). (English) Zbl 1234.41008 East J. Approx. 17, No. 2, 171-179 (2011). The present paper deals with the extension technique which allows to deduce inequalities involving regular moduli of smoothness on a bounded domain in \(\mathbb R^d\) from inequalities involving moduli of smoothness of periodic functions on \(T^d=[-\pi,\pi]^d\). The goal is to apply the extension technique to establish sharp lower estimates for moduli of smoothness on bounded Lipschitz-graph domains in \(\mathbb R^d\) for rearrangement-invariant Banach function spaces satisfying certain conditions. These inequalities give an significant improvement over the classical immediate estimate \(\omega^{r+1}(f,t)_B\leq 2\omega^r(f,t)_B\). Reviewer: Vijay Gupta (New Delhi) Cited in 1 Document MSC: 41A25 Rate of convergence, degree of approximation 41A17 Inequalities in approximation (Bernstein, Jackson, Nikol’skiĭ-type inequalities) Keywords:modulus of smoothness; Banach function spaces; Orlicz spaces PDFBibTeX XMLCite \textit{Z. Ditzian} and \textit{A. Prymak}, East J. Approx. 17, No. 2, 171--179 (2011; Zbl 1234.41008)