积分交换 meaning in English

integral transform

In the first chapter , we obtained weighted norm inequality on the commutators , by proving a variant of sharp function estimates ; j . orobitg and c . perez introduced ap weights for nondoubing measures and proved weighted norm inequality of c - z singular integrals . in the second chapter , we obtained weighted inequalities of fractional integral and its maximal function with ap ( u ) weights for nondoubing measure ; e . sawyer obtained a weak type double weights inequality for fractional integrals in [ 13 ] . in the third chapter , we generalized the sawyer ' s result for non - doubling measures
本文第一章通过证明一个变形的sharp估计，从而得到奇异积分交换子的加权有界性； j . orobitg和c . p rez在文[ 10 ]中引入了非倍测度的a _ p权理论并证明了c - z奇异积分的加权有界性，本文第二章得到了分数次积分算子和分数次极大函数在非倍测度下a _ p ( )权的加权估计； e . sawyer在文[ 13 ]中得到了分数次积分的一个双权弱型不等式，本文第三章把e . sawyer的结果推广到非倍测度的情形。