沿复合曲线的粗糙核参数型Marcinkiewicz积分算子的有界性

Parametric Marcinkiewicz Integrals with Rough Kernels Supported by Compound Subvarieties

研究沿复合曲线的粗糙核参数型Marcinkiewicz积分算子,在积分核满足相当弱的尺寸条件下,建立了这些算子的L^p有界性.作为应用,相应于面积积分和Littlewood-Paley-g_λ~*函数的参数型Marcinkiewicz积分算子的L^p有界性也被给出.

In this paper, we establish the L^p boundedness for a class of rough parametric Marcinkiewiez integral operators associated with polynomial compound mappings, under rather weaker size conditions on the kernels, which essentially improve and generalize certain previous results. As applications, the L^p bounds of the corresponding parametric Marcinkiewicz integral ooerators related to area integrals and Littlewnncl-Palev g＊λ functionare also botained.