Ding, Chunmei; Yang, Ruyue; Cao, Feilong The strong converse inequality for de la Vallée Poussin means on the sphere. (English) Zbl 1334.41016 J. Comput. Anal. Appl. 20, No. 1, 34-41 (2016). Summary: This paper discusses the approximation by de la Vallée Poussin means \(V_nf\) on the unit sphere. Especially, the lower bound of approximation is studied. As a main result, the strong converse inequality for the means is established. Namely, it is proved that there are constants \(C_1\) and \(C_2\) such that \(C_1\omega(f,\frac1{\sqrt{n}})_p\leq\|V_nf-f\|_p\leq C_2\omega(f,\frac1{\sqrt{n}})_p\) for any \(p\)th Lebesgue integrable or continuous function \(f\) defined on the sphere, where \(\omega(f,t)_p\) is the modulus of smoothness of \(f\). Cited in 1 Document MSC: 41A25 Rate of convergence, degree of approximation 42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) Keywords:approximation; modulus of smoothness; lower bound PDFBibTeX XMLCite \textit{C. Ding} et al., J. Comput. Anal. Appl. 20, No. 1, 34--41 (2016; Zbl 1334.41016) Full Text: arXiv