Riesz位势算子范数不等式及其推广

Riesz Potential Operator Norm Inequalities and Its Generalizations

如何求出Riesz位势算子不等式中的最佳常数,一直是还没有完全解决的难题.本文通过将求最佳常数问题转化为求相应的算子范数等新的分析技巧,得到了Riesz位势算子的范数不等式.作为它的推广,得到了n维向量空间上具有径向核的新的积分算子范数不等式.

How to obtain the sharp constant of the Riesz potential operator inequality remains unsolved. In this paper, by means of the new analysis technique of the sharp constant factor is changed into the corresponding operator norm, the Riesz potential operator norm inequalities are proved. As its generalizations, some new operator norm inequalities with radial kernel on n-dimensional vector spaces are established.