Studies On A Class Of Hankel Tensors And Their Properties

In this paper,we mainly discuss the properties of finite and infinite dimensional Hankel tensors.We proved the relationship between infinite dimensional Hankel tensor and Carleson measure on Hadry spaces,and obtained some upper or lower bounds of Frobenius norm and lp norm of Cauchy-Hankel tensors.This paper is divided into three sections:In section 1,we introduce the basic concepts of Hankel tensor,Cauchy-Hankel tensor,Hilbert tensor and norm,and their research status.In section 2,we explore some properties of m order infinite-dimensional Hankel tensor on analytic function space.We introduce the concepts of Hadry space and Carleson measure,and then by the properties of Carleson measure,we obtained that the relation between Hankel tensor and Carleson measure on Hardy space.In section 3,we introduce the concepts of Gamma function and its derivative functions and get the lower bound of Frobenius norm of m order n dimension Cauchy-Hankel tensor by Gamma function.Moreover,the concepts of m order infinite dimension Cauchy-Hankel tensor and lp norm are introduced and some upper bounds are obtained.