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非倍测度空间上的插值定理和多线性分数次积分算子
The Interpolation Theorem and Multilinear Fractional Integral Operator on Non-doubling Measure Spaces
【作者】 连佳丽；
【导师】 伍火熊；
【作者基本信息】 厦门大学 ， 基础数学， 2008， 硕士
【摘要】 本论文主要研究非倍测度空间上的插值定理和多线性分数次积分算子及其交换子的有界性。全文共分两章,第一章致力于研究伴随非倍测度μ的Hardy空间上的插值定理,其中μ为满足某种增长性条件的非负Radon测度。我们建立了一个新的插值定理,该定理改进了Tolsa在[25]的插值定理。第二章,我们研究一类由多线性分数次积分和RBMO(μ)函数生成的交换子,借助于Sharp极大函数估计,建立了该类算子在赋予测度μ的Lebesgue乘积空间上的有界性,推广了谌稳固和Sawyer在[3]的结果。
【Abstract】 This dissertation is devoted to the study of the interpolation theorem related to Hardy spaces and the boundedness of multilinear fractional integral operator and its commutators in non-doubling measure spaces. It consists of two chapters.The first chapter is concerning with the interpolation theorem on Hardy space associated toμ, whereμis the nonnegative Radon measure satisfying some growth condition. We establish a new interpolation theorem which improves the interpolation theorem of Tolsa in [25].Chapter 2 deals with a class of commutators generated by multilinear fractional integrals and RBMO(μ) functions. The boundedness of such operators on product of Lebesgue spaces withμare established, which extends the result of Chen and Sawyer in [3].