Institute of Metrology and Computational Science, China Jiliang University, Hangzhou 310018, Zhejiang Province, China
Academic Editor: S. S. Dragomir
Copyright © 2011 Shaobo Lin and Feilong Cao. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
In the paper titled as “Jackson-type inequality on the sphere” (2004), Ditzian introduced a spherical nonconvolution operator , which played an important role in the proof of the well-known Jackson inequality for spherical harmonics. In this paper, we give the lower bound of approximation by this operator. Namely, we prove that there are constants and such that for any th Lebesgue integrable or continuous function defined on the sphere, where is the th modulus of smoothness of .