双弦幂积分不等式的注记

设K为R^d中的有界凸体，σ1，σ2分别为K被随机直线G1，G2截得的弦长，则称Lm,n（K）=∫G1ηG2∈κσ1^mσ2^ndG1DG2为凸体K关于m，n的双弦幂积分，双弦幂积分是积分几何中弦幂积分概念的推广，经典的等周不等式、弦幂积分完全不等式、R^d中弦幂积分统一不等式都隶属于双弦幂积分不等式范畴，故研究关于双弦幂积分的不等式具有重大意义。利用线偶的运动不变密度、Holder不等式及Schwarz不等式，得到几个关于双弦幂积分的不等式，即文中的（7）、（10）、（12）、（16）、（17）、（22）和（23）式。

Some Notes on the Double Chord-power Integral

Set K to R^d the bounded convex body, σ1,σ2 respectively is random linear section G1, G2 chord length Im,n（K） =∫G1ηG2∈κσ1^mσ2^ndG1DG2is called a convex body K about the m,n double chord-power integrals, double chord-power integrals is integralgeometry chord-power integrals in the promotion of the concept of classic isoperimetric inequality, chord-power integrals inequality completely, unification of chord-power integrals Re are affiliated to the double chord-power integrals inequality category, so the re- search about the inequality of the double chord-power integrals is of great significance. We use line coupling movement constant den- sity, H61der inequation, Schwarz inequality, got several inequalities o{ the double chord-power integrals of the （7）, （10）, （12）, （16） and （17）, （22） and （23）.