Potential analysis

潜力分析

• 批准号: 15340046
• 负责人: AIKAWA Hiroaki
• 金额: $ 5.38万
• 依托单位: Hokkaido University (2005-2006)Shimane University (2003-2004)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2006
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-15340046/
• 关键词: capacity density condition; harmonic measure; harmonic function; uniform domain; Bergman space; Dirac equation; Sobolev function; parabolic equation; 関数微分方程式; 内部一様領域; Carleson評価; Fatou定理; 熱方程式

・Under the capacity density condition, we characterize uniform domains, inner uniform domains and John domains in terms of the boundary Hamack principle and estimates of harmonic measure.・We study the bounday behavior of non-integrable kernel and derive the Fatou type theorem and Littlewood type theorem.・We show the 3G-inequality for inner uniform domains. We construct a domain whose Martin boundary and topological boundary coincide, and yet the Cranston-McConnell inequality, and as a result, the 3G- inequality fail to hold in case the dimension is greater than or equal 3.・We show the equivalence between the boundary Hamack principle and the Carleson estimate.・For a smooth doimain in the Euclid space. we show the boundary Harnack principle for p-harmonic func- tion.・We give the Carleson estomates for p-harmonic functions.・We give conditions for the p-Dirichlet solution of a Holder continuos boundary function to be Hoder continuos up tp the boundary.・We study the Martin boundary of a John domain. By the John constant, we estimate the number of minimal Martin boundary points over a topological boundary.

・在容量密度条件下，利用边界 Hamack 原理和调和测度估计来刻画均匀域、内均匀域和 John 域 ・研究不可积核的边界行为，推导出 Fatou 型定理和 Littlewood。类型定理。・我们展示了内部均匀域的 3G 不等式我们构造了一个马丁边界和拓扑边界重合的域，但仍然存在 Cranston-McConnell 不等式，因此 3G 不等式失败。在维数大于或等于 3 的情况下保持。 ・我们展示了边界哈马克原理和卡尔森估计之间的等价性。 ・对于欧几里得空间中的光滑域，我们展示了 p 调和函数的边界哈纳克原理。・我们给出了 p 调和函数的 Carleson 估计。 ・我们给出了 Holder 连续边界函数的 p-Dirichlet 解为 Hoder 连续 up tp 的条件・我们研究约翰域的马丁边界，通过约翰常数，我们估计拓扑边界上的最小马丁边界点的数量。

项目成果

LP-boundedness of Bergman projections for a-parabolic operators

a-抛物线算子的 Bergman 投影的 LP 有界性

• 发表时间: 2006
• 期刊: Advanced Studies in Pure Mathematics 44
• 作者: M.Nishio;K.Shimomura;N.Suzuki
• 通讯作者: N.Suzuki

Martin boundary and boundary Hamack principle for non-smooth domains

非光滑域的马丁边界和哈马克边界原理

• 发表时间: 2005
• 期刊: Amer. Math. Transl. (2), 215
• 作者: Y.Mizuta;T.Shimomura;H.Aikawa
• 通讯作者: H.Aikawa

K.Shimomura, N.Suzuki, M.Nishio: "α-parabolic Bergman spaces and their reproducing kernels"数理解析研究所講究録. 1352. 106-113 (2004)

K.Shimomura、N.Suzuki、M.Nishio：“α-抛物线伯格曼空间及其再现核”数学科学研究所 Kokyuroku。1352. 106-113 (2004)

Some observations of approximation of fixed points of nonexpansive nonself- mappings

非扩张非自映射不动点近似的一些观察

• 发表时间: 2003
• 期刊: Proceedings of the Second International Conference on Nonlinear Analysis and Convex Analysis
• 作者: S.Matsushita;D.Kuroiwa
• 通讯作者: D.Kuroiwa

N.Suzuki, N.A.Watson: "Mean value densities for temperatures"Colloquium Mathematicum. 98. 87-96 (2003)

N.Suzuki，N.A.Watson：“温度的平均值密度”数学研讨会。