粗糙核抛物型奇异积分算子与外插  

Parabolic singular integrals with rough kernels and extrapolation

作　　者：刘风[1] 伍火熊[1] 

机构地区：[1]厦门大学数学科学学院,厦门361005

出　　处：《中国科学：数学》2014年第5期519-534,共16页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11071200和11371295)资助项目

摘　　要：本文研究粗糙核抛物型奇异积分算子及其极大算子.借助精细的Fourier变换估计和LittlewoodPaley理论,并结合外插讨论,在积分核满足球面Hardy函数条件和相当弱的径向尺寸条件下,本文建立这些算子的Lp有界性.进一步,关于沿一般光滑曲面的奇异积分算子及其极大算子的相应结果也被建立.这些结果即使在迷向情形也是新的.This paper is devoted to studying the parabolic singular integrals with rough kernels both on the unit sphere and in the radial direction, as well as the corresponding maximal singular integrals. By the estimates of Fourier transforms, the Littlewood-Paley theory and the extrapolation arguments, under the rather weak size conditions, which are the best known ones so far, the applications, the corresponding results for the corresponding also obtained. L^p bounds for such operators are established. As operators associated to certain smooth surfaces are

关 键 词：奇异积分 极大算子 混合齐性 粗糙核 外插 

分 类 号：O177.6[理学—数学]