紧致齐性空间上的调和分析（Ⅳ）─—Riesz变换与Bessel变换

Harmonic Analysis on Compact Homogeneous Spaces (Ⅳ)──The Riesz and Bessel Transformations

本文研究了紧致齐性空间上的Ｒｉｅｓｚ位势算子与Ｂｅｓｓｅｌ位势算子，Ｒｉｅｓｚ变换与Ｂｅｓｓｅｌ变换，给出了上述算子对应的核函数的具体构造并证明了Ｒｉｅｓｚ变换与Ｂｅｓｓｅｌ变换作为奇异积分算子的Ｈ￣ｐ有界性，ｐ＞０。

The Riesz and Bessel potential operators and Riesz and Bessel transformations oncompact homogeneous spaces are discussed in this paper. Furthermore,we construct concretekernel functions for these operators and we prove the H￣p(M)boundedness for these operatorsfor p>0. Especially, we proved that the Riesz and Bessel transformations, as singular integrals,are H￣p bounded for p>0.