变指数Herz-Hardy空间上的多线性算子

发布时间：2018-06-16 21:21

本文选题：多线性算子 + Riesz位势　；参考：《青岛大学》2017年硕士论文

【摘要】：本文首先介绍了变指数Lebesgue空间的基本概念、性质和某些奇异积分算子在变指数Lebesgue空间的有界性.然后,利用变指数Lebesgue空间的概念和Calderon-Zygmund多线性奇异积分算子、多线性分数次积分的性质,基于变指数Herz-Hardy空间上的原子分解定理,利用Holder不等式和Jensen不等式,证明了从变指数乘积Herz-Hardy空间到变指数Herz空间上的Calderon-Zygmund多线性奇异积分算子和多线性Riesz位势的有界性.
[Abstract]:In this paper, we first introduce the basic concepts and properties of variable exponential Lebesgue spaces and the boundedness of some singular integral operators in variable exponential Lebesgue spaces. Then, by using the concept of variable exponent Lebesgue space and the properties of Calderon-Zygmund multilinear singular integral operator and multilinear fractional integral, based on the atomic decomposition theorem on the variable exponent Herz-Hardy space, Holder inequality and Jensen inequality are used. The boundedness of Calderon-Zygmund multilinear singular integral operator and multilinear Riesz potential from the variable exponential product Herz-Hardy space to the variable exponential Herz space is proved.
【学位授予单位】：青岛大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O177

【参考文献】