[[[[[ List of Publications -- Eiichi Nakai ]]]]]

[[[[[ book ]]]]]
  1. Editors Akihiko Miyachi, Eiichi Nakai and Masami Okada, Harmonic Analysis and its Applications, 2006, Yokohama Publishers.
    ISBN 4-946552-20-0
  2. M. Hasumi, H. Oka, N. Sakakibara and E. Nakai, Introduction to Calculus (Japanese), Uchida R\^okakuho, Tokyo, 1998.
    ISBN 4-7536-0095-5

[[[[[ papers ]]]]]
  1. Yoshihiro Mizuta, Eiichi Nakai, Yoshihiro Sawano and Tetsu Shimomura Littlewood-Paley theory for variable exponent Lebesgue spaces and Gagliardo-Nirenberg inequality for Riesz potentials, Journal of the Mathematical Society of Japan, to appear. Article in Press
  2. Yasuo Komori-Furuya, Katsuo Matsuoka, Eiichi Nakai and Yoshihiro Sawano Integral operators on B_{\sigma}-Morrey-Campanato spaces, Revista Matematica Complutense, Published online, 29 December 2011 Online First DOI:10.1007/s13163-011-0091-6
  3. Yoshihiro Mizuta, Eiichi Nakai, Takao Ohno and Tetsu Shimomura, Maximal functions, Riesz potentials and Sobolev embeddings on Musielak-Orlicz-Morrey spaces of variable exponent in $\R^n$, Revista Matematica Complutense, Published online 31 May 2011 Online First DOI:10.1007/s13163-011-0074-7
  4. Eiichi Nakai and Yoshihiro Sawano, Hardy spaces with variable exponents and generalized Campanato spaces, Journal of Functional Analysis Volume 262, Issue 9 (1 May 2012), 3665--3748. ScienceDirect DOI:10.1016/j.jfa.2012.01.004
  5. Eiichi Nakai and Tsuyoshi Yoneda, Bilinear estimates in dyadic BMO and the Navier-Stokes equations, Journal of the Mathematical Society of Japan, Volume 64, Number 2 (April 2012), 399--422. Article in Press
  6. Takashi Miyamoto, Eiichi Nakai and Gaku Sadasue, Martingale Orlicz-Hardy spaces, Mathematische Nachrichten, Volume 285, Issue 5-6 (April 2012), 670--686. Wiley Online Library DOI:10.1002/mana.201000109
  7. Yoshihiro Mizuta, Eiichi Nakai, Yoshihiro Sawano and Tetsu Shimomura, Gagliardo-Nirenberg inequality for generalized Riesz potentials of functions in Musielak-Orlicz spaces, Archiv der Mathematik, Volume 98, Number 3 (March 2012), 253-263. SpringerLink DOI:10.1007/s00013-012-0362-6
  8. Katsuo Matsuoka and Eiichi Nakai, Fractional integral operators on $B^{p,\lambda}$ with Morrey-Campanato norms, Function Spaces IX (Krakow, Poland, 2009), 249--264, Banach Center Publications , Vol.92, Institute of Mathematics, Polish Academy of Sciences, Warszawa, 2011. Banach Center Publications DOI:10.4064/bc92-0-17
  9. Yoshihiro Mizuta, Eiichi Nakai, Takao Ohno and Tetsu Shimomura, Sobolev's inequality for Riesz potentials in Orlicz-Musielak spaces of variable exponent, Banach and Function Spaces III (Kitakyushu, 2009), 409--419, Yokohama Publishers, Yokohama, 2011.
  10. Eiichi Nakai, Orlicz-Morrey spaces and their preduals, Banach and Function Spaces III (Kitakyushu, 2009), 187--205, Yokohama Publishers, Yokohama, 2011.
  11. Haibo Lin, Eiichi Nakai and Dachun Yang, Boundedness of Lusin-area and $g_{\lambda}^*$ functions on localized Morrey-Campanato spaces over doubling metric measure spaces, Journal of Function Spaces and Applications, Volume 9 (2011), Issue 3, 245--282. Open Access DOI:10.1155/2011/187597
  12. Yoshihiro Mizuta, Eiichi Nakai, Takao Ohno and Tetsu Shimomura, Riesz potentials and Sobolev embeddings on Morrey spaces of variable exponent, Complex Variables and Elliptic Equations, Vol.56, Issue 7-9 (July 2011), 671--695. Taylor and Francis Online DOI:10.1080/17476933.2010.504837
  13. Yoshihiro Mizuta, Eiichi Nakai, Takao Ohno and Tetsu Shimomura, Hardy's inequality in Orlicz-Sobolev spaces of variable exponent, Hokkaido Mathematical Journal, Vol.40, No.2 (June 2011), 187--203.
  14. Eiichi Nakai and Tsuyoshi Yoneda, Riesz transforms on generalized Hardy spaces and a uniqueness theorem for the Navier-Stokes equations, Hokkaido Mathematical Journal, Vol.40, No.1 (February 2011), 67--88.
  15. Haibo Lin, Eiichi Nakai and Dachun Yang, Boundedness of Lusin-area and $g_{\lambda}^*$ functions on localized BMO spaces over doubling metric measure spaces, Bulletin des Sciences Mathematiques, Vol.135, No.1 (January-February 2011), 59--88. ScienceDirect DOI:10.1016/j.bulsci.2010.03.004
  16. Lech Maligranda and Eiichi Nakai, Pointwise multipliers of Orlicz spaces, Archiv der Mathematik, Vol.95, No.3 (September, 2010), 251--256. SpringerLink DOI:10.1007/s00013-010-0160-y
  17. Yoshihiro Mizuta, Eiichi Nakai, Takao Ohno and Tetsu Shimomura, Boundedness of fractional integral operators on Morrey spaces and Sobolev embeddings for generalized Riesz potentials, Journal of the Mathematical Society of Japan, Vol.62, No.3 (July, 2010), 707--744. Project Euclid Article in Press, Journal of MSJ DOI:10.2969/jmsj/06230707
  18. Eiichi Nakai, Singular and fractional integral operators on Campanato spaces with variable growth conditions, Revista Matematica Complutense, Vol.23, No.2 (July, 2010) 355--381. SpringerLink DOI:10.1007/s13163-009-0022-y
  19. Shigehiko Kuratsubo, Eiichi Nakai and Kazuya Ootsubo, Generalized Hardy identity and relations to Gibbs-Wilbraham and Pinsky phenomena, Journal of Functional Analysis, Vol.259 (July, 2010), 315--342. ScienceDirect DOI:10.1016/j.jfa.2010.03.025
  20. Yan Meng, Eiichi Nakai and Dachun Yang, Estimates for Lusin-area and Littlewood-Paley $g^*_{\lambda}$ functions over spaces of homogeneous type, Nonlinear Anal., Vol.72, No.5 (March, 2010), 2721--2736. ScienceDirect DOI:10.1016/j.na.2009.11.019
  21. Eiichi Nakai and Tsuyoshi Yoneda, Construction of solutions for the initial value problem of a functional-differential equation of advanced type, Aequationes Mathematicae, Vol.77, No. 3 (June, 2009), 259-272. SpringerLink DOI:10.1007/s00010-009-2965-y
  22. Yoshihiro Mizuta, Eiichi Nakai, Takao Ohno and Tetsu Shimomura, An elementary proof of Sobolev embeddings for Riesz potentials of functions in Morrey spaces $L^{1,\nu,\beta}(G)$, Hiroshima Mathematical Journal, Vol.38 (2008), 425-436. Project Euclid
  23. Eiichi Nakai, A generalization of Hardy spaces $H^p$ by using atoms, Acta Mathematica Sinica, Vol.24 (2008), 1243--1268. SpringerLink DOI:10.1007/s10114-008-7626-x
  24. Eiichi Nakai, Orlicz-Morrey spaces and the Hardy-Littlewood maximal function, Studia Mathematica, Vol.188, No.3 (2008), 193--221. Studia Mathematica DOI:10.4064/sm188-3-1
  25. Eiichi Nakai, Calder\'on-Zygmund operators on Orlicz-Morrey spaces and modular inequalities, Banach and Function Spaces II (Kitakyushu, 2006), 393--410, Yokohama Publishers, Yokohama, 2008.
  26. Eiichi Nakai, Recent topics of fractional integrals, Sugaku Expositions, American Mathematical Society, Vol.20, No.2 (2007), 215--235. Osaka Kyoiku University Repository
  27. Norio Kikuchi, Eiichi Nakai, Naohito Tomita, K\^oz\^o Yabuta and Tsuyoshi Yoneda, Calder\'on-Zygmund operators on amalgam spaces and in the discrete case, Journal of Mathematical Analysis and Applications, Vol.335 (2007), 198--212. ScienceDirect DOI:10.1016/j.jmaa.2007.01.043
  28. Eiichi Nakai, The Campanato, Morrey and H\"older spaces on spaces of homogeneous type, Studia Mathematica, Vol.176, No.1 (2006), 1--19. Studia Mathematica DOI:10.4064/sm176-1-1
  29. Shigehiko Kuratsubo, Eiichi Nakai and Kazuya Ootsubo, On the Pinsky Phenomenon of Fourier Series of the Indicator Function in Several Variables, Memoirs of Osaka Kyoiku University, Ser.III Natural Science and Applied Science Vol.55, No.1 (2006), 1--20. Osaka Kyoiku University Repository
  30. Eiichi Nakai, Construction of an atomic decomposition for functions with compact support, Journal of Mathematical Analysis and Applications, Vol.313 (2006), 730--737. ScienceDirect DOI:10.1016/j.jmaa.2005.07.072
  31. Eiichi Nakai, Generalized fractional integrals on Orlicz-Morrey spaces, Banach and Function Spaces (Kitakyushu, 2003), 323--333, Yokohama Publishers, Yokohama, 2004.
  32. Eiichi Nakai, Recent topics of fractional integrals (Japanese), Sugaku Vol.56 (2004), 260--280. Journal@rchive Osaka Kyoiku University Repository
  33. Eridani, Hendra Gunawan and Eiichi Nakai, On generalized fractional integral operators, Scientiae Mathematicae Japonicae, Vol.60 (2004), 539--550. (Scientiae Mathematicae Japonicae Online, Vol.10 (2004), 307--318.)
  34. Eiichi Nakai, Naohito Tomita and K\^oz\^o Yabuta, Density of the set of all infinitely differentiable functions with compact support in weighted Sobolev spaces, Scientiae Mathematicae Japonicae, Vol.60 (2004), 121--127. (Scientiae Mathematicae Japonicae Online, Vol.10 (2004), 39--45.)
  35. Eiichi Nakai and Shigeo Okamoto, Tangential boundary behavior of the Poisson integrals of functions in the potential space with the Orlicz norm, Scientiae Mathematicae Japonicae, Vol.59 (2004), 407--428. (Scientiae Mathematicae Japonicae Online, Vol.9 (2003), 187--208.)
  36. Eiichi Nakai, On generalized fractional integrals on the weak Orlicz spaces, $BMO_{\phi}$, the Morrey spaces and the Campanato spaces, Function spaces, interpolation theory and related topics (Lund, 2000), 389--401, Walter de Gruyter, Berlin, New York, 2002. de Gruyter Reference Global eBook ISBN: 9783110198058
  37. Chikako Harada and Eiichi Nakai, The square partial sums of the Fourier transform of radial functions in three dimensions, Scientiae Mathematicae Japonicae, Vol.55 (2002), 467--477. (Scientiae Mathematicae Japonicae Online, Vol.5 (2001), 329--339.)
  38. Eiichi Nakai, On generalized fractional integrals, Taiwanese Journal of Mathematics, Vol.5 (2001), 587--602.
  39. Eiichi Nakai, On generalized fractional integrals in the Orlicz spaces on spaces of homogeneous type, Scientiae Mathematicae Japonicae, Vol.54 (2001), 473--487. (Scientiae Mathematicae Japonicae Online, Vol.4 (2001), 901--915.)
  40. Eiichi Nakai and Hironori Sumitomo, On generalized Riesz potentials and spaces of some smooth functions, Scientiae Mathematicae Japonicae, Vol.54 (2001), 463--472. (Scientiae Mathematicae Japonicae Online, Vol.4 (2001), 891--900.)
  41. Eiichi Nakai, A characterization of pointwise multipliers on the Morrey spaces, Scientiae Mathematicae, Vol.3 (2000), 445--454.
  42. Eiichi Nakai, On generalized fractional integrals in the Orlicz spaces, Proceedings of the Second ISAAC Congress, Kluwer Academic Publishers B. V. Netherland-U. S. A., 2000, 75--81.
  43. Eiichi Nakai, Pointwise multipliers on the Morrey Spaces, Memoirs of Osaka Kyoiku University, Ser.III Natural Science and Applied Science Vol.46 (1997), 1--11. Osaka Kyoiku University Repository
  44. Eiichi Nakai, Pointwise multipliers on weighted BMO spaces, Studia Mathematica, Vol.125, No.1 (1997), 35--56. Studia Mathematica
  45. Eiichi Nakai and K\^oz\^o Yabuta, Pointwise multipliers for functions of weighted bounded mean oscillation on spaces of homogeneous type, Mathematica Japonica, Vol.46 (1997), 15--28.
  46. Eiichi Nakai, Pointwise multipliers on the Lorentz Spaces, Memoirs of Osaka Kyoiku University, Ser.III Natural Science and Applied Science Vol.45 (1996), 1--7. Osaka Kyoiku University Repository
  47. Eiichi Nakai, Pointwise multipliers, Memoirs of The Akashi College of Technology, Vol.37 (1995), 85--94.
  48. Eiichi Nakai, Hardy-Littlewood maximal operator, singular integral operators and the Riesz potentials on generalized Morrey spaces, Mathematische Nachrichten, Vol.166 (1994), 95--103. InterScience DOI:10.1002/mana.19941660108
  49. Eiichi Nakai, Pointwise multipliers for functions of weighted bounded mean oscillation, Studia Mathematica, Vol.105, No.2 (1993), 105--119. Studia Mathematica
  50. Eiichi Nakai and K\^oz\^o Yabuta, Singular integral operators on $L^{p,\Phi}$-spaces, Annali di Matematica pura ed applicata, Vol.153 (1988), 53--62. SpringerLink
  51. Eiichi Nakai, Singular integral operators on $L_k^{p,\Phi}$-spaces, Bulletin of the Faculty of Science, Ibaraki University, Series A. Mathematics, Vol.19 (1987), 71--78. Journal@rchive
  52. Eiichi Nakai and K\^oz\^o Yabuta, Pointwise multipliers for functions of bounded mean oscillation, Journal of the Mathematical Society of Japan, Vol.37, No.2 (1985), 207--218. Project Euclid DOI:10.2969/jmsj/03720207
  53. Eiichi Nakai, On the restriction of functions of bounded mean oscillation to the lower dimensional space, Archiv der Mathematik, Vol.43 (1984), 519--529. SpringerLink

[[[[[ others ]]]]]
  1. Eiichi Nakai, Predual of Campanato spaces and Riesz potentials} Potential Theory and its related Fields (Japanese), S\=urikaisekikenky\=usho K\=oky\=uroku No. 1669 (November, 2009), 122--131.
  2. Eiichi Nakai and Tsuyoshi Yoneda, Convergence of some truncated Riesz transforms on predual of generalized Campanato spaces and its application to a uniqueness theorem for nondecaying solutions of Navier-Stokes equations. The geometrical structure of Banach spaces and Function spaces and its applications (Japanese), S\=urikaisekikenky\=usho K\=oky\=uroku No. 1667 (November, 2009), 71--79.
  3. Eiichi Nakai, A generalization of Hardy spaces on spaces of homogeneous type, Recent results of Banach and function spaces and its applications (Japanese), S\=urikaisekikenky\=usho K\=oky\=uroku No. 1615 (October, 2008), 99--106.
  4. Eiichi Nakai, Preduals of Morrey-Campanato spaces, Banach spaces, function spaces, inequalities and their applications (Japanese), S\=urikaisekikenky\=usho K\=oky\=uroku No. 1570 (2007), 46--53. Kyoto University Research Information Repository
  5. Eiichi Nakai, On Orlicz-Morrey spaces, The structure of Banach spaces and Function spaces (Japanese), S\=urikaisekikenky\=usho K\=oky\=uroku No. 1520 (2006), 78--88. Kyoto University Research Information Repository Osaka Kyoiku University Repository
  6. Eiichi Nakai, Naohito Tomita and K\^oz\^o Yabuta, Fourier multipliers and decomposition of functions by convolution, Communication in commutative Banach algebras and several field of mathematics (Japanese), S\=urikaisekikenky\=usho K\=oky\=uroku No. 1478 (2006), 116--126. Kyoto University Research Information Repository Osaka Kyoiku University Repository
  7. Eiichi Nakai, Naohito Tomita and K\^oz\^o Yabuta and Tsuyoshi Yoneda, Boundedness of singular integral operators on some Morrey and amalgam spaces (Japanese), Banach and function spaces and their application (Japanese), S\=urikaisekikenky\=usho K\=oky\=uroku No. 1455 (2005), 128--136. Kyoto University Research Information Repository Osaka Kyoiku University Repository
  8. Eiichi Nakai, Naohito Tomita and K\^oz\^o Yabuta, Extensions of Fig`a-Talamanca's multiplier theorem to Banach function spaces, Banach and function spaces and their application (Japanese), S\=urikaisekikenky\=usho K\=oky\=uroku No. 1455 (2005), 1--7. Kyoto University Research Information Repository Osaka Kyoiku University Repository
  9. Eiichi Nakai, Orlicz-Morrey spaces and some integral operators, The structure of Banach spaces and its application (Japanese) S\=urikaisekikenky\=usho K\=oky\=uroku No. 1399 (2004), 144--156. Kyoto University Research Information Repository Osaka Kyoiku University Repository
  10. Eiichi Nakai, Hardy spaces and generalized fractional integrals, Harmonic Analysis and Nonlinear Partial Differential Equations, S\=urikaisekikenky\=usho K\=oky\=uroku No. 1388 (2004), 1--22. Kyoto University Research Information Repository Osaka Kyoiku University Repository
  11. Eiichi Nakai, Hardy spaces and preduals of Campanato spaces (Japanese), Harmonic/analytic function spaces and linear operators, II (Japanese), S\=urikaisekikenky\=usho K\=oky\=uroku No. 1277, (2002), 67--77. Kyoto University Research Information Repository Osaka Kyoiku University Repository
  12. Eiichi Nakai, Generalized fractional integrals, S\=urikaisekikenky\=usho K\=oky\=uroku No. 1201 (2001), 56--74. Kyoto University Research Information Repository Osaka Kyoiku University Repository
  13. Eiichi Nakai, Pointwise multipliers on some function spaces (Japanese), Proceedings of Chowa-Kaiseki Seminar 2000 (Japanese), 99--118.
  14. Eiichi Nakai, On generalized fractional integrals, S\=urikaisekikenky\=usho K\=oky\=uroku No. 1137, (2000), 61--70. Kyoto University Research Information Repository Osaka Kyoiku University Repository
  15. Eiichi Nakai, Pointwise multipliers on Campanato spaces and Morrey spaces (Japanese), Harmonic/analytic function spaces and linear operators (Japanese) (Kyoto, 1998), S\=urikaisekikenky\=usho K\=oky\=uroku No. 1049 , (1998), 1--10. 46E30 (46M35). Kyoto University Research Information Repository Osaka Kyoiku University Repository
  16. Eiichi Nakai, BMO and related function spaces on spaces of homogeneous type (Japanese), Proceedings of Jitsukansuron-kansukaisekigaku godo symposium 36 (1997), 94--123.
  17. Eiichi Nakai, Weighted BMO on homogeneous spaces (Japanese), The structure of spaces of analytic and harmonic functions and the theory of operators on them (Japanese) (Kyoto, 1995), S\=urikaisekikenky\=usho K\=oky\=uroku No. 946 , (1996), 141--151. 42B15. Kyoto University Research Information Repository Osaka Kyoiku University Repository
  18. Eiichi Nakai and K\^oz\^o Yabuta, Pointwise multipliers on $\mathrm{bmo}_{\phi}(\mathbb R^n)$ (Japanese), S\=urikaisekikenky\=usho K\=oky\=uroku No. 523 (1984), 192--207.