理论数学  >> Vol. 3 No. 1 (January 2013)

实单位球上的面积积分算子
Area Integral Operator on the Real Unit Ball

DOI: 10.12677/PM.2013.31010, PDF, HTML, 下载: 2,936  浏览: 11,750  国家自然科学基金支持

作者: 王东方*:湖南大学数学与计量经济学院;马柏林, 沈丹桂*:嘉兴学院数理与信息工程学院

关键词: 面积积分算子Carleson测度单位球单位球面Area Integral Operator; Carleson Measure; The Unit Ball; The Unit Sphere

摘要: 本文通过Carleson boxes或者Tents的方式定义了实单位球上的Carleson测度,并建立了单位球上非切极大函数、Poisson积分和Carleson测度之间的联系。作为一个应用,我们引入一种中单位球体上非负测度相关的面积积分算子,并用Carleson测度和其他方式刻画了这种使得或从有界的非负测度
Abstract: In this paper, we introduce Carleson measures on the real unit ball in terms of Carleson boxes or tents, and establish relations among the non-tangential maximal function, Poisson integral and Carleson measures on the real unit ball. As an application, we introduce a certain area integral operator involving a nonnegative measure on the unit ball and characterize the measure in terms of Carleson measure and other forms such that maps from to or from to .

文章引用: 王东方, 马柏林, 沈丹桂. 实单位球上的面积积分算子[J]. 理论数学, 2013, 3(1): 56-67. http://dx.doi.org/10.12677/PM.2013.31010

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