Clifford分析中具有超正则核的T算子的性质 |
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引用本文: | 马韶瑜,乔玉英,杨贺菊.Clifford分析中具有超正则核的T算子的性质[J].数学的实践与认识,2014(1). |
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作者姓名: | 马韶瑜 乔玉英 杨贺菊 |
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作者单位: | 河北师范大学数学与信息科学学院;河北科技大学理学院; |
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基金项目: | 国家自然科学基金(11301136);河北省自然科学基金(A2010000346) |
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摘 要: | 讨论了Clifford分析中具有超正则核的T(Ieodorescu)算子的基本性质.T算子是定义在区域上的奇异积分算子,它在广义解析函数理论和Vekua理论中起着重要的作用.在复分析中关于T算子的理论已经发展得很完善,但在Clifford分析中,具有超正则核的T算子的相关性质还没有得到研究.研究了Clifford分析中具有超正则核的T算子的基本性质,得到了这个算子在ΩR_+~(n+1)上的一致有界性,Hlder连续性以及这个算子的γ次可积性.
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关 键 词: | 超正则函数 Teodorescu算子 一致有界性 Hlder连续性 γ次可积性 |
The Properties of T-operator with Hypermonogenic kernel in Clifford Analysis |
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Abstract: | The basic properties of the T(Teodorescu) operator with hypermonogenic kernel in Clifford analysis are studied in this paper.T-operator is a singular integral operator defined in a domain and it plays an important role in generalized analytic function and Vekua theory.In Complex analysis,many theories about T-operator are well development.But in Clifford analysis,it hasn't been studied about the properties of a T-operator with hypermonogenic kernel.The paper focuses on the basic properties of T-operator which has hypermonogenic kernel in Clifford analysis.We obtain its uniform boundedness and Holder continuity in ΩR_+~(n+1) space.At the same time we also prove the 7 times integrability of the operator. |
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Keywords: | hypermonogenic function teodorescu operator uniform boundedness Hlder continuity γ times integrability |
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