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，我们根据边界hamack原理和谐波测量的估计来表征均匀的域，内部均匀域和约翰域。 ・我们研究了不可积分内核的边界行为，并得出了FATOU型定理和Littlewood型定理。 ・我们显示了内部均匀结构域的3G毒性。我们构建了一个领域，其马丁的边界和拓扑边界重合，但克兰斯顿·麦康奈尔不平等，结果，如果维度大于或等于3，则3G不平等无法保持3G-不平等。 func-tion。・我们给出了p谐波功能的Carleson估计值。我们给出了持有人持续边界函数的p-dirichlet解决方案的条件，以继续hoder继续tp tp。・我们研究了约翰域的马丁边界。通过约翰·康斯坦德（John Constant），我们估计马丁边界的最小数量指向拓扑边界。

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。