The L ~ P - Dimension Unrelated Estimation Of Riesz Transforms On Modified AN Groups (p> 1)

The master dissertation is concerned with the Lp(p>1)-estimates of Riesz trans-form on harmonic AN groups. And the Lp(p>1)-estimates can be taken to be inde-pendent of the dimension. The structure of this paper is as follows.Chapter Ⅰ:Preface. This chapter is devoted to introduce the basic structure of harmonic AN groups, the definition of Riesz transform on Riemannian manifold and the history of research in Lp(p>1)-estimates of Riesz transform. The main results of this master dissertation are brief introduced in this chapter.Chapter Ⅱ:The Ricci curvature of harmonic AN groups. Firstly, we will give the definition of Ricci curvature. Secondly, we will calculate the Ricci curvature of harmonic AN groups.Chapter Ⅲ:LP(p>1)-estimates which are independent of the dimension for Riesz transform on harmonic AN groups. In this chapter, we will give some knowledge about spectral resolution and heat kernel. Then, we will prove that the Lp(p>1)-estimates of Riesz transform can be taken to be independent of the dimension on harmonic AN groups.