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| 球面S~(d-1)上的广义Ul'yanov型不等式 | |
| 引用本文： | 王晟. 球面S~(d-1)上的广义Ul'yanov型不等式[J]. 数学学报, 2011, 54(1): 115-124 |
| 作者姓名： | 王晟 |
| 作者单位： | 1. 北京师范大学数学科学学院 北京 100875; 2. 桂林电子科技大学数学与计算科学学院 桂林 541004 |
| 基金项目： | 国家自然科学基金资助项目(10771016) |
| 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. |
| 关 键 词： | 球调和 分数阶导数 连续模 广义Ul'yanov型不等式 |
| 收稿时间： | 2010-03-25 |
| 修稿时间： | 2010-07-23 |
Generalized Ul'yanov Type Inequality on the Sphere Sd-1 |
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| Sheng WANG. Generalized Ul'yanov Type Inequality on the Sphere Sd-1[J]. Acta Mathematica Sinica, 2011, 54(1): 115-124 | |
| Authors: | Sheng WANG |
| Affiliation: | 1. School of Mathematical Sciences, Beijing Normal University, Beijing 100875, P. R. China; 2. School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541004, P. R. China |
| Abstract: | 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. |
| Keywords: | spherical harmonics fractional derivatives moduli of smoothness generalized Ul&rsquo yanov-type inequalities |
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