Multiple Hardy–Littlewood Integral Operator Norm Inequalities

How to obtain the sharp constant of the Hardy–Littlewood inequality remains unsolved. In this paper, the new analytical technique is to convert the exact constant factor to the norm of the corresponding operator, the multiple Hardy–Littlewood integral operator norm inequalities are proved. As its generalizations, some new integral operator norm inequalities with the radial kernel on n-dimensional vector spaces are established. The discrete versions of the main results are also given.