【作者】 孙建国；

【导师】 陶双平；

【作者基本信息】 西北师范大学 ， 应用数学， 2009， 硕士

【摘要】 本文分四章,研究了几类(次)线性算子及其高阶交换子和多线性交换子在截口上的有界性.第一章得到了由BMOF(Rn)函数和核K(x,y)满足一定截口条件的奇异积分算子H生成的高阶交换子Hbm(f)的加权估计第二章得到了由BMOF(Rn)函数和核K(x,y)满足一定截口条件的奇异积分算子H生成的多线性交换子Hb(f)的加权估计.第三章主要讨论了非二倍测度下截口上的分数次积分算子Iαf(x)的有界性,并且得到了增长条件是上述结论成立的必要条件.第四章主要讨论了一类次线性算子及其交换子在截口上的Morrey空间Lp,λ(Rn)上的有界性.更多还原

【Abstract】 The core of this thesis, which consists of four chapters, mainly studies the boundednes properties of several classes of (sub)linear operators and higher order commutators and multilinear commutators associated with the sections.In chapter 1, we obtain the weighted estimates for higher order commutators which are generated by singular integral operators with kernel K(x, y) which satisfies some sections conditions and BMOF(Rn) functions.In chapter 2, we obtain the weighted estimates for multilinear commutators which are generated by singular integral operators with kernel K(x, y) which satisfies some sections conditions and BMOF(Rn) functions.In chapter 3, we mainly discuss the boundedness of the fractional integral operators associated to the sections for non-doubling measures. Furthermore, we also prove that the growing conditionμ(S(x, r))≤Crn,Vx∈Rn, r> 0 is a necessary condition for the above results.In chapter 4, we mainly establish the boundedness in the Morrey spaces for the sections for a class of sublinear operators and commutators更多还原