Some Researchs On Sharp Hardy Type Inequality

In the fields of mathematics and physics,Hardy-type inequalities play an important role,so it is necessary to conduct in-depth research on Hardy-type inequalities and promote them.In this paper,the Hardy inequality with the average distance function,the related Hardy inequality in the hyperbolic space,and the Hardy inequality related to the Jacobi operator are studied in this paper.The specific research content of this article are:1.Hardy inequality with the average distance function multiply a distance function to obtain the result.2.Using the Picone identity obtain the Pocincaré-Hardy indquality over the entire area,and get the weighted result.3.Combine Hardy inequality with Jacobi operator and use a special constructor to get the weighted Hardy inequality and prove that the constant is the best constant.