中文摘要：

本文对于单位球面上的经典连续模，给出了一个非常有用的广义Ul’yanov型不等式．该不等式在球面多项式逼近、球面嵌入理论以及球面上函数空间的插值理论等领域有着非常重要的应用．我们的证明基于球面调和多项式展开的新的估计，这些估计本身也具有独立的意义．

英文摘要：

We prove a generalized Ul＇yanov type inequality for the classical moduli of smoothness on the unit sphere, which has important applications in imbedding theory, spherical polynomial approximation and the theory of interpolation in function spaces on the sphere. Our proof is based on several new estimates on spherical harmonic expansions, which seem to be of independent interest.