The Study of caloric morphism

热量态射的研究

• 批准号: 17540144
• 负责人: SHIMOMURA Katsunori
• 金额: $ 1.73万
• 依托单位: Ibaraki University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2005
• 资助国家: 日本
• 起止时间: 2005 至 2006
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-17540144/
• 关键词: caloric morphism; Appell transformation; heat equation; 熱方程式

The purpose of this research is the study of the caloric morphism (the transformation which preserve the solution of the heat equation), focusing on the explicit determination of the morphism.We obtained the following results in the term of the project.1. We have determined the caloric morphism for constant curvature spaces.2. We determined all the caloric morphism between two semi-euclidean spaces with different radial metrics. As a result, we found a new type of caloric morphism in this setting, whose space mapping is the mixture of the similarity and the inversion.3. We made the list of fundamental caloric morphisms between two semi-euclidean spaces with different radial metrics. And we gave a representation of all the caloric morphism as a composition of the fundamental caloric morphisms.

这项研究的目的是对热量形态的研究（保留热方程解的转换），重点是对形态的明确确定。我们在项目期限内获得了以下结果。1。我们已经确定了恒定曲率空间的热量形态。2。我们确定了两个具有不同径向指标的半欧亚裔空间之间的热量形态。结果，我们在这种情况下发现了一种新型的热量形态，其空间映射是相似性和反转的混合物3。我们列出了两个具有不同径向指标的半欧亚人空间之间的基本热量形态。我们将所有热量形态的代表作为基本热量形态的组成。

项目成果

Toeplitz operators and Carleson measures on parabolic Bergman space.

托普利茨算子和卡尔森在抛物线伯格曼空间上进行测量。

• 期刊: Hokkaido Math. J. (印刷中)
• 作者: M.Nishio;N.Suzuki;M.Yamada
• 通讯作者: M.Yamada

$L^p$-boundedness of Bergman profections for $alpha$-parabolic operators

$alpha$-抛物线算子的 Bergman 投影的 $L^p$-有界性

• 期刊: Advanced Studies in Pure Math. (掲載決定)
• 作者: Masaharu Nishio;Katsunori Shimomura;Noriaki Suzuki
• 通讯作者: Noriaki Suzuki

Sharp remainder terms of Hardy-Sobolev inequalities.

Hardy-Sobolev 不等式的锐余项。

• 发表时间: 2005
• 期刊: Math.J.Ibaraki Univ. 37(印刷中)
• 作者: A.Detalla;T.Horiuchi;H.Ando
• 通讯作者: H.Ando

Carleson type measures on parabolic of Bergman spaces

伯格曼空间抛物线的卡尔森型测度

• 发表时间: 2006
• 期刊: J.Math.Soc.Japan 58
• 作者: Masaharu Nishio;Masahiro Yamada
• 通讯作者: Masahiro Yamada

Caloric morphism with respect to radial metrics on semi-euclidean spaces

半欧几里得空间上径向度量的热量态射

• 发表时间: 2005
• 期刊: Math.J.Ibaraki univ. 37
• 作者: G.Nakamura;N.Suzuki;Osamu Hatori;Takeshi Miura;Katsunori Shimomura
• 通讯作者: Katsunori Shimomura