Katsunori SHIMOMURAProfessor
■Researcher basic information
Organization
- College of Science Department of Sciences Mathematics and Informatics
- Graduate School of Science and Engineering（Master's Program） Major in Science
- Graduate School of Science and Engineerin（Doctoral Program） Major in Complex Systems Science
- Faculty of Basic Natural Science Domain of Mathematics and Informatic
Career
■Research activity information
Paper
- Relations between Morrey–Campanato spaces and the duals of atomic Hardy spaces
Satoshi Yamaguchi; Eiichi Nakai; Katsunori Shimomura, Springer Science and Business Media LLC
Archiv der Mathematik, 20 Mar. 2025, [Reviewed] - Bi-predual Spaces of Generalized Campanato Spaces with Variable Growth Condition
Satoshi Yamaguchi; Eiichi Nakai; Katsunori Shimomura, Springer Science and Business Media LLC
Acta Mathematica Sinica, English Series, 20 Dec. 2024, [Reviewed] - A remark on the dual spaces of bi-parabolic Bergman spaces
Yôsuke Hishikawa; Masaharu Nishio; Katsunori Shimomura; Masahiro Yamada, Corresponding, Department of Mathematics, Faculty of Science
Mathematical Journal of Ibaraki University, Dec. 2023, [Reviewed] - Rational function and time transformation of caloric morphism on semi-euclidean spaces
Katsunori Shimomura
Mathematical Journal of Ibaraki University, Dec. 2021, [Reviewed] - Function spaces induced by two parabolic Bloch spaces
Y. Hishikawa; M. Nishio; K. Shimomura; M. Yamada, Hiroshima University - Department of Mathematics
Hiroshima Mathematical Journal, Nov. 2021, [Reviewed] - Reproducing property for iterated parabolic operators of fractional order.
M. Nishio; K. Shimomura, Ed. Acad. Române
Mathematical Reports (Bucuresti), Jul. 2021, [Reviewed] - Existence and non-existence of caloric morphisms with Bateman space-mapping for radial metrics.
Katsunori Shimomura
Mathematical Journal of Ibaraki University, Jul. 2019, [Reviewed] - Reproducing Kernels for Iterated Parabolic Operators on the Upper Half Space with Application to Polyharmonic Bergman Spaces
Masaharu Nishio; Katsunori Shimomura
COMPLEX ANALYSIS AND OPERATOR THEORY, Dec. 2017, [Reviewed] - Liouville type theorem on conformal mapping for indefinite metrics associate with ultra-hyperbolic equations
Katsunori Shimomura
Mathematical Journal of Ibaraki University, Sep. 2016, [Reviewed] - Generalizations of Bateman's transformation for general indefinite metrics
Katsunori Shimomura, Batemans transformation is associated with the Lorentzian metric and preserves solutions of the wave equation. We generalize Batemans transformation for general indefinite semi-euclidean metrics. Then we show that the generalized transformation preserves solutions of the equation associated with given indefinite metric., Department of Mathematics, Faculty of Science, Ibaraki University
Mathematical Journal of Ibaraki University, May 2013, [Reviewed] - A relation between the Lorentzian inversion and the Bateman transformation
Katsunori Shimomura, In our previous paper [1], we proved that every transformation which preserves the wave equation is a similarity or a Lorentzian inversion composed with similarities or a Bateman transformation composed with similarities. In this paper, we give several relations between Bateman transformation and Lorentzian inversion. We also prove that only Lorentzian inversion or Bateman transformation is enough to generate the set of all transformations which preserve the wave equation., College of Science, Ibaraki University
Mathematical Journal of Ibaraki University, May 2012, [Reviewed] - Liouville type theorem associate with the wave equation
Katsunori Shimomura, College of Science, Ibaraki University
Mathematical Journal of Ibaraki University, May 2011, [Reviewed] - Caloric morphisms between different radial metrics on semi-euclidean spaces of same dimension
Katsunori Shimomura, This paper generalizes and improves the result of [8] to caloric morphisms between manifolds with different radial semi-euclidean metrics. It is based on the similar arguments as were used in [7] and [8] (cf. [4], [5], [6]), but it succeed to remove the technical assumption from the main result of [8]., College of Science, Ibaraki University
Mathematical Journal of Ibaraki University, May 2011, [Reviewed] - Caloric Morphisms for rotation invariant metrics.
Masaharu Nishio; Katsunori Shimomura, Lead
Hiroshima Mathematical Journal, Nov. 2010, [Reviewed] - $L^p$-boundedness of Bergman projections for $\alpha$-parabolic operators (共著)
Masaharu Nishio; Katsunori Shimomura; Noriaki Suzuki
Advanced Studies in Pure Mathematics, 2006, [Reviewed] - Caloric morphisms with respect to radial metrics on semi-euclidean spaces
Katsunori Shimomura, Faculty of Science, Ibaraki University
Mathematical Journal of Ibaraki University, May 2005, [Reviewed] - Caloric morphisms with respect to radial metrics on $\mathbb R^n \setminus \{0\}$
Katsunori Shimomura, Faculty of Science, Ibaraki University
Mathematical Journal of Ibaraki University, May 2003, [Reviewed] - A characterization of caloric morphisms between manifolds (共著)
M. Nishio; K. Shimomura, Lead
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica., 2003, [Reviewed] - Caloric morphisms on semi-euclidean space.
M. Nishio; K. Shimomura, Lead
Revue Roumaine de Mathematiques pures et Appliquees, 2002, [Reviewed] - On transformations which preserve poly-temperatures of degree m
Katsunori Shimomura, Ibaraki University
Mathematical Journal of Ibaraki University, 2001, [Reviewed] - The Determination of Caloric Morphisms on Euclidean Domains.
Katsunori Shimomura
Nagoya Mathematical Journal, 2000, [Reviewed] - Note on Poly-Supertemperatures on a Strip Domain
M. Nishio; K. Shimomura; N. Suzuki
Osaka Journal of Mathematics, 1999, [Reviewed] - A Mean Value Property of Poly-temperatures on a Strip Domain
M. Nishio; K. Shimomura; N. Suzuki
Journal of the London Mathematical Society, 1998, [Reviewed] - Caloric morphisms and a generalization of the Appell transformation
Katsunori Shimomura
Proceedings of the Seventh International Colloquium on Differential Equations, VSP, 1997 - A general form of a mean value property for poly-temperatures on a strip domain
M. Nishio; K. Shimomura; N. Suzuki
Proceedings of the Seventh International Colloquium on Differntial Equations, VSP, 1997 - The Growth of the Positive Solutions of Lu=0 near the Boundary of an Inner NTA Domain
Katsunori Shimomura
Nagoya Mathematical Journal, 1988, [Reviewed]
MISC
- $\alpha$-parabolic Bergman spaces and their reproducing kernels (Applications of the theory of reproducing kernels)
Shimomura Katsunori; Suzuki Noriaki; Nishio Masaharu
RIMS Kokyuroku, Jan. 2004 - A Characterization of the Inner NTA Domain by the Quasi-hyperbolic metric
Katsunori Shimomura
Bulletin of the Faculty of Science Ibaraki University, 1992 - A note on the definition of inner NTA domain
Katsunori Shimomura
Bulletin of the Faculty of Science Ibaraki University, 1991
Books and other publications
Lectures, oral presentations, etc.
- On the dual spaces of polyparabolic Bergman spaces via reproducing formulae
下村勝孝
2024年度ポテンシャル論研究集会, 07 Dec. 2024 - A remark on the dual spaces of bi-parabolic Bergman spaces
下村勝孝
2022年度ポテンシャル論研究集会, 10 Feb. 2023
20230210, 20230212 - 半Euclid空間上のcaloric morphismの時間変換と実有理関数
下村勝孝
日本数学会2022年度年会, 28 Mar. 2022, 日本数学会
20220328, 20220331 - 半ユークリッド空間上の Caloric morphism の時間変換と実有理関数
下村勝孝
2021年度ポテンシャル論研究集会, 11 Feb. 2022, 日本数学会函数論分科会ポテンシャル論研究グループ, [Invited]
20220211, 20220212 - ユークリッド空間上の caloric morphism の時間変換
下村勝孝
2019年度ポテンシャル論研究集会, 13 Oct. 2019, 日本数学会函数論分科会ポテンシャル論研究グループ, [Invited]
20191013, 20191014 - Caloric morphism ― 熱方程式の解を保つ変換
下村勝孝
日本数学会2019年度秋季総合分科会 特別講演, 17 Sep. 2019, 日本数学会, [Invited]
20190917, 20190920 - Time transformations of caloric morphisms on Euclidean spaces
下村勝孝
Potential Analysis and its Related Fields 2019, 13 Feb. 2019, [Invited]
20190212, 20190213 - Bateman変換とCaloric morphism
下村勝孝
2018年度ポテンシャル論研究集会, 01 Sep. 2018, [Invited]
20180831, 20180902 - Caloric morphisms for rotation invariant metrics on semi-euclidean spaces
Katsunori SHIMOMURA
AIMS 2018 Taipei, 08 Jul. 2018, American Institution Mathematical Sciences, [Invited]
20180705, 20180709 - Caloric morphism with Bateman space mapping for radial metrics
下村勝孝
日本数学会秋季総合分科会, 11 Sep. 2017, 日本数学会
20170911, 20170914 - Caloric morphism with Bateman space mapping for radial metrics
下村勝孝
ポテンシャル論研究集会, 01 Sep. 2017, 日本数学会函数論分科会ポテンシャル論研究グループ, [Invited]
20170831, 20170902 - Caloric morphism ― 熱方程式の解を保つ変換
下村勝孝
第59回函数論シンポジウム, 09 Oct. 2016, 日本数学会函数論分科会, [Invited]
20161008, 20161010 - Lorentz不変形量に対する caloric morphism について
下村勝孝
ポテンシャル論研究集会, 06 Sep. 2016, 日本数学会函数論分科会ポテンシャル論研究グループ, [Invited]
20160905, 20160907 - 3次元以上のLorentz不変計量に対する caloric morphism について
下村勝孝
研究集会「ポテンシャル論とその関連分野」, 31 Jan. 2016, [Invited]
20160131, 20160201 - 非正定値計量の等角写像について
ポテンシャル論研究集会, 04 Nov. 2011, 日本数学会函数論分科会ポテンシャル論研究グループ, [Invited]
20111103, 20111105 - 非正定値計量の等角写像に対するLiouville型の定理
ポテンシャル論研究集会, 06 Nov. 2010, 日本数学会函数論分科会ポテンシャル論研究グループ, [Invited]
20101105, 20101107 - 異なる動径方向計量を持つ半ユークリッド空間の間の Caloric morphism
ポテンシャル論研究集会, 03 Nov. 2008, 日本数学会函数論分科会ポテンシャル論研究グループ, [Invited]
20081101, 20081103 - Caloric morphism for rotation invariant metric on Euclidean spaces
Katsunori Shimomura
Finland-Japan Joint Seminar on Analysis, 29 Aug. 2007
20070827, 20070829 - Rn (n≧3) の回転不変計量に関するcaloric morphism
下村勝孝; 西尾昌治
日本数学会2007年度年会, 29 Mar. 2007, 日本数学会
20070327, 20070330 - 回転不変な計量に関するcaloric morphism
下村勝孝
ポテンシャル論研究集会, 12 Jan. 2007, 日本数学会函数論分科会ポテンシャル論研究グループ, [Invited]
20070111, 20070112 - 回転不変な計量に関する caloric morphism
下村勝孝
ポテンシャル論とその関連分野, 20 Dec. 2006, 京都大学数理解析研究所, [Invited]
20061218, 20061220 - Caloric morphism on manifolds
Masaharu Nishio; Katsunori Shimomura
Finland-Japan Joint Seminar on Analysis, 14 Dec. 2006, [Invited] - Caloric morphism for two radial metrics
Katsunori Shimomura
The Tenth Conference on Real and Complex Analysis in Hiroshima, 03 Nov. 2006, [Invited]
20061102, 20061104 - 二つの半ユークリッド空間の動径方向計量に関するcaloric morphism
下村勝孝
日本数学会2006年度秋期総合分科会, 19 Sep. 2006, 日本数学会
20060919, 20060922 - Caloric morphism for rotation invariant metric
Katsunori Shimomura
The Ninth conference on Real and Complex Analysis in Hiroshima, 15 Dec. 2005, [Invited] - Caloric morphism
Katsunori Shimomura
Mathematisches Kolloquium, KU Eichstaett, 16 Nov. 2005, Mathematisch-Geographische Fakultaet, Katholi-sche Universitaet Eichstaett - Caloric morphism for rotation invariant metric.
下村勝孝
ポテンシャル論研究集会, 05 Nov. 2005 - 半ユークリッド空間の動径方向計量に関するcaloric morphism
下村勝孝
日本数学会2005年度秋期総合分科会, 21 Sep. 2005, 日本数学会 - ∂/∂t - (-Δ)α に対するBergman空間の再生核の Lp-有界性
下村勝孝; 鈴木紀明; 西尾昌治
日本数学会2005年度秋期総合分科会, 19 Sep. 2005, 日本数学会 - The caloric morphism for radial metrics on semi-euclidean spaces
Katsunori Shimomura
International Workshop on Potential Theory in Matsue 2004, 27 Aug. 2004 - Lp-boundedness of Bergman projections for α-parabolic operators
Masaharu Nishio; Katsunori Shimomura; Noriaki Suzuki
International Workshop on Potential Theory in Matsue 2004, 27 Aug. 2004 - α-parabolic Bergman spaces and their reproducing kernels
下村勝孝; 鈴木紀明; 西尾昌治
再性核の理論の応用, Oct. 2003
Research Themes
- A new refinement allowing infinite-order degeneration and explosion of weighted classical inequalities and its application to variational problems
Grant-in-Aid for Scientific Research (C)
Ibaraki University
Apr. 2020 - Mar. 2025 - Potential theory for parabolic equations and related function spaces
Grant-in-Aid for Scientific Research (C)
Apr. 2019 - Mar. 2023 - 古典的不等式の精密化に基づく非線型楕円型方程式の定性的研究
Grant-in-Aid for Scientific Research (C)
Ibaraki University
Apr. 2016 - Mar. 2020
