Rchr

J-GLOBAL ID：200901086769471170 Update date: Apr. 09, 2024

NAKAI Eiichi

ナカイエイイチ | NAKAI Eiichi

Affiliation and department：
Job title： Project Researcher
Homepage URL (1)： http://enakai.sci.ibaraki.ac.jp/

Research field (2)： Mathematical analysis , Basic analysis

Research theme for competitive and other funds (39)：

2021 - 2026 平均振動量・増大度が一様でない関数空間の理論と応用
2020 - 2025 A new refinement allowing infinite-order degeneration and explosion of weighted classical inequalities and its application to variational problems
2020 - 2025 一般調和解析に由来する増大条件を伴う関数空間の深化と展開
2020 - 2025 調和解析における実関数論の方法とその応用
2019 - 2022 種々のマルティンゲール空間とその上の分数べき積分作用素および交換子

2017 - 2022 多変数フーリエ級数の収束問題とガウスの円問題

2017 - 2022 Wienerの一般調和解析に端を発する関数空間の深化と展開

2016 - 2020 Qualitative study of nonlinear elliptic equations based on refinement of classical inequalities

2015 - 2020 Deepening of theory of function spaces from real and harmonic analysis and its application

2016 - 2019 Study of martingale spaces and martingale inequalities in view of real analysis

2012 - 2016 New development in non-commutative harmonic analysis related to singular integrals - A fusion of representation theory and real analysis

2012 - 2016 Refinement of classical inequalities and its application to elliptic variational problems

2012 - 2015 Structures of some martingale spaces, and operators on these martingale spaces

2012 - 2015 Harmonic analysis based on function spaces with variable exponent and its applications

2011 - 2015 Harmonic analysis by real variable methods and its applications

2010 - 2012 On some contact points with the multiple Fourier series and lattice point problems with weights

2008 - 2011 Theory of Singular Integral Operators in Non-commutative Harmonic Analysis. A verification of Use of Real Hardy Spaces.

2008 - 2011 Function spaces with variable exponent

2008 - 2011 On the improvement of classical inequalities and its applications to nonlinear degenerate elliptic equations

2006 - 2009 Harmonic analysis by real variable methods and its applications

2007 - 2008 Study of singular integrals and function spaces

2006 - 2007 Study of Multilinear singular Integral and Littlewood-Paley Operator

2005 - 2007 On the linearization of quasilinear degenerate elliptic equations and the structure of singular solutions

2006 - 2006 実解析を用いた信号及び画像解析における共同研究の調査

2005 - 2006 一般化Morrey-Campanato空間の前相対空間

2005 - 2006 Micorlocal filtering using wavelet and local multiresolution analysis

2003 - 2004 Microlocal filtering with wavelet frames multiresolution analysis

2002 - 2004 Entropy on non-commutative dynamical systems and the structure of operator algebras

2002 - 2004 On the structure of singular solutions for degenerate elliptic equations

2001 - 2003 Weight theory related to harmonic analysis on groups -in harmony with representation theory

2002 - 2002 調和解析研究グループの構築と共同研究の企画

2001 - 2002 Microlocal filtering with multiwavelet frames

2000 - 2001 Entropy in the non-commutalrive dynamical systems and the structure of algebras

1999 - 2001 Theory and applications of BMO and related function spaces on spaces of homogeneous type

1999 - 2001 The research on degenerate elliptic partial differential equations by the method of real analysis

1997 - 1999 Entropy for automorphisms of operator algebras

1996 - 1996 homogeneous型空間上の重み付きBMO

1995 - 1995 クンツ型自己準同型写像

1994 - 1994 BMOとこれに関連した函数空間上での各点的マルチプライヤーについて

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Papers (94)：

Eiichi Nakai. The convergence problem of multiple Fourier series and Gauss's circle problem. Nihon University College of Economics, Research Bulletin. 2023. 98. 139-157
Ryota Kawasumi, Eiichi Nakai and Minglei Shi. Characterization of the boundedness of generalized fractional integral and maximal operators on Orlicz-Morrey and weak Orlicz-Morrey spaces. Mathematische Nachrichten. 2023. 296. 4. 1483-1503
Amagai, Kohei; Nakai, Eiichi; Sadasue, Gaku;. Generalized Fractional Integral Operators Based on Symmetric Markovian Semigroups with Application to the Heisenberg Group. Taiwanese Journal of Mathematics. 2023. 27. 1. 113-139
Satoshi Yamaguchi, Eiichi Nakai. Compactness of Commutators of Integral Operators with Functions in Campanato Spaces on Orlicz-Morrey Spaces. Journal of Fourier Analysis and Applications. 2022. 28. 2. Paper No.33-32pp
Mitsuo Izuki, Eiichi Nakai and Yoshihiro Sawano. Atomic and wavelet characterizations of Musielak--Orlicz Hardy spaces for generalized Orlicz functions. Integral Equations and Operator Theory. 2022. 94. 1. Article 3, 33pp

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MISC (5)：

中井英一, 貞末岳. Fractional integrals on martingale spaces (関数空間の構造とその周辺). 数理解析研究所講究録. 2017. 2041. 220-226
IZUKI Mitsuo, NAKAI Eiichi, SAWANO Yoshihiro. Hardy spaces with variable exponent (Harmonic Analysis and Nonlinear Partial Differential Equations). RIMS Kokyuroku Bessatsu. 2013. 42. 109-136
Nakai Eiichi, Sadasue Gaku. Martingale Morrey-Campanato spaces (Banach space theory and related topics). RIMS Kokyuroku. 2011. 1753. 58-66
Eiichi Nakai. Recent topics of fractional integrals. Sugaku Expositions. 2007. 20. 2. 215--235-235
NAKAI E. On generalized fractional integrals on the weak Orlicz spaces, BMO_φ, the Morrey spaces and the Campanato spaces. Function spaces, interpolation theory and related topics (Lund, 2000). 2002

Books (2)：

Harmonic Analysis and its Applications
Yokohama Publishers 2006 ISBN:4946552200
解析入門
内田老鶴圃 1998 ISBN:4753600955

Lectures and oral presentations (18)：

Generalized Campanato spaces with variable growth condition and related topics
(MSJ Autumn Meeting 2023 2023)
Bi-preduals of generalized Campanato spaces with variable growth condition
(MSJ Autumn Meeting 2023 2023)
On the critical Caffarelli-Kohn-Nirenberg type inequalities involving super-logarithms
(MSJ Autumn Meeting 2023 2023)
Bi-predual spaces of Campanato spaces and integral operators
(2023)
Generalized Campanato spaces with variable growth condition and related topics
(MSJ Spring Meeting 2023 2023)

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Professional career (2)：

理学修士 (茨城大学)
Doctor (Nara Women's University)

Committee career (7)：

2012/03 - 現在国際数理科学協会 SCIENTIAE MATHEMATICAE JAPONICAE 編集委員
2010/04 - 現在インドネシア数学会 Journal of the Indonesian Mathematical Society 編集委員
2011/04 - 2023/03 Department of Mathematics, Ibaraki University Editor of Mathematical Journal of Ibaraki University
2021/03 - 2022/02 The Mathematical Society of Japan Councilor
2011/07 - 2015/06 日本数学会数学編集委員

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Awards (1)：

2022/09 - The Mathematical Society of Japan The 2022 MSJ Analysis Prize Harmonic analysis on generalized Morrey-Campanato spaces and related studies

Association Membership(s) (2)：

International Society for Mathematical Sciences , The Mathematical Society of Japan

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