The strong converse inequality for de la Vallée Poussin means on the sphere.

This paper discusses the approximation by de la Vallée Poussin means Vnf 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 C1 and C2 such that C1ω (f, 1/√n) p ≤ ‖Vnf - f‖p ≤ C2ω (f, 1/√n) p for any p-th Lebesgue integrable or continuous function f defined on the sphere, where ω(f, t)p is the modulus of smoothness of f. [ABSTRACT FROM AUTHOR]