Endpoint Estimates And Q-integral Inequality Of Hardy Operators

In this paper,we mainly study the endpoint estimation of Hardy operators on one dimension and n dimension and extend and improve the existing Hardy operator properties.Firstly,the necessity of Hardy operators to limit some indices is verified by special functions.Secondly,we connect Hardy operator with q integral inequality to find the constants and prove the optimality of its operator norm.In the first chapter,the development background of Hardy operators is briefly introduced,and the existing simple definitions and corresponding theorems of Hardy operators in one dimension and n dimension are introduced.At the same time,some endpoint estimation theorems and q integral inequality theorems of more optimized Hardy operators are given.In the second chapter,we give the proof of Hardy operator’s endpoint estimation.In chapter 3,the boundedness of the theorem is proved by using q integral methods.In chapter 4,we continue to promote Hardy operator with q integral inequality and prove the optimality of its constant existence.