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, We consider parabolic operators of fractional order and their iterates on the upper half space of the euclidean space. We deal with Hilbert spaces of solutions of those parabolic equations. We shall show, in this note, the existence of reproducing kernels and give a formula by using their fundamental solutions. As an application, we also discuss the polyharmonic Bergman spaces and give their reproducing kernels by using the Poisson kernel on the upper half space., SPRINGER BASEL AG
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, We determine all the caloric morphisms for rotation invariant (spherically symmetric) metrics, in the case where the space dimension is greater than two. We also treat the caloric morphisms on two dimensional spheres and hyperbolae., HIROSHIMA UNIV, GRAD SCH SCI
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]

α-parabolic bergman spaces. (共著)
M. Nishio; K. Shimomura; N. Suzuki, The alpha-parabolic Bergman space b(alpha)(p) is the set of all p-th integrable solutions U of the equation (partial derivative/partial derivative t + (-Delta)(alpha))u = 0 on the upper half space, where 0 < alpha <= 1 and 1 <= p <= infinity. The Huygens property for the above u will be obtained. After verifying that the space b(alpha)(p) forms a Banach space, we discuss the fundamental properties. For example, as for the duality, (b(alpha)(p))* congruent to b(alpha)(q) for p > 1 and (b(alpha)(l))* congruent to B-alpha/R are shown, where q is the exponent conjugate to p and B-alpha is the alpha-parabolic Bloch space., OSAKA JOURNAL OF MATHEMATICS
Osaka J. Math., 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, In this paper, we give a characterization of mappings which preserve caloric functions between semi-riemannian manifolds., SUOMALAINEN TIEDEAKATEMIA
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, Let D be a domain in Rm+1 and E be a domain in Rn+1. A pair of a smooth mapping f : D --> E and a smooth positive function rho on D is called a caloric morphism if rho . u o f is a solution of the heat equation in D whenever u is a solution of the heat equation in E. We give the characterization of caloric morphisms, and then give the determination of caloric morphisms. In the case of m < n there are no caloric morphisms. In the case of m = n; caloric morphisms are generated by the dilation, the rotation, the translation and the Appell transformation. In the case of m > n: under some assumption on f, every caloric morphism is obtained by composing a projection with a direct sum of caloric morphisms of Rn+1., NAGOYA UNIV
Nagoya Mathematical Journal, 2000, [Reviewed]

Note on Poly-Supertemperatures on a Strip Domain
M. Nishio; K. Shimomura; N. Suzuki, OSAKA JOURNAL OF MATHEMATICS
Osaka Journal of Mathematics, 1999, [Reviewed]

A Mean Value Property of Poly-temperatures on a Strip Domain
M. Nishio; K. Shimomura; N. Suzuki, LONDON MATH SOC
Journal of the London Mathematical Society, 1998, [Reviewed]

Caloric morphisms and a generalization of the Appell transformation
Katsunori Shimomura, We give a systematic way to construct caloric morphisms between different dimensional Euclidean spaces., VSP BV-C/O BRILL ACAD PUBL
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, We show that the mean value property of poly-temperature, the solution of the iterate of the heat operator, also holds for more general mean value than that of [1]., VSP BV-C/O BRILL ACAD PUBL
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 UNIV
Nagoya Mathematical Journal, 1988, [Reviewed]

$\alpha$-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

関数解析の基礎　　　　　　　　　　　　　　　
堀内利郎; 下村勝孝, Joint work
内田老鶴圃, 10 Apr. 2005
9784753600991

線形代数入門　　　　　　　　　　　　　　　
荷見守助; 下村勝孝, Joint work
内田老鶴圃, 10 Apr. 2002
9784753600984

複素解析の基礎　　　　　　　　　　　　　　　
堀内利郎; 下村勝孝, Joint work
内田老鶴圃, 10 Apr. 2001
9784753600977

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 L^p-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

L^p-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

2006 - 2016
茨城大学

Sep. 1985, Mathematical Society of Japan

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