学术报告（杨东勇 3.2）

摘要： Let $\lambda \in (-1/2, \infty)$. Consider the following two operators on $R_+=(0,\infty)$:

   $$\Delta_\lambda=-\frac{d^2}{dx^2}-\frac{2\lambda}{x} \frac{d}{dx},

     S_\lmabda=-\frac{d^2}{dx^2}+\frac{\lambda^2-\lambda}{x^2}.$$

 In this talk, we will discuss the Lp -boundedness of oscillations, variations and Littlewood-Paley functions, associated with $\Delta_\lambda$ and $ S_\lmabda $ respectively. We will also discuss endpoint cases and weighted cases. These results are based on some joint works with Xuan Thinh Duong et al..