Last modified on 14/10/2011

Books

  1. H. Aikawa, Minimal thinness and the Beurling minimum principle, in Around the research of Vladimir Maz'ya. III, Vol. 13 of Int. Math. Ser. (N. Y.), Springer, New York (2010), 25-46, 2664704 (2011f:31013), preprint , ARTICLE

  2. H. Aikawa, Boundary Harnack principle and the quasihyperbolic boundary condition, in Sobolev spaces in mathematics. II, Vol. 9 of Int. Math. Ser. (N. Y.), Springer, New York (2009), 19-30, MR2484620 (2010b:31009), preprint , ARTICLE

  3. H. Aikawa, T. Kumagai, Y. Mizuta, and N. Suzuki eds., Potential theory in Matsue, Vol. 44 of Advanced Studies in Pure Mathematics, Mathematical Society of Japan, Tokyo (2006), Papers from the International Workshop on Potential Theory held at Shimane University, Matsue, August 23-28, 2004, MR2265403, preprint

  4. H. Aikawa and M. Essén, Potential theory--Selected topics, Vol. 1633 of Lecture Notes in Mathematics, Springer-Verlag, Berlin (1996), MR1439503 (98f:31005)

Articles

  1. H. Aikawa, Modulus of continuity of the Dirichlet solutions, Bull. Lond. Math. Soc., 42, 5 (2010), 857-867, 2721745 (2011g:31009), preprint , ARTICLE

  2. H. Aikawa, Equivalence between the boundary Harnack principle and the Carleson estimate, Math. Scand., 103, 1 (2008), 61-76, MR2464701 (2009j:31008), preprint

  3. H. Aikawa and K. Hirata, Doubling conditions for harmonic measure in John domains, Ann. Inst. Fourier (Grenoble), 58, 2 (2008), 429-445, MR2410379 (2009c:31009), preprint , ARTICLE

  4. H. Aikawa, T. Kilpeläinen, N. Shanmugalingam, and X. Zhong, Boundary Harnack principle for p-harmonic functions in smooth Euclidean domains, Potential Anal., 26, 3 (2007), 281-301, MR2286038 (2008a:31012), preprint , ARTICLE

  5. H. Aikawa, K. Hirata, and T. Lundh, Martin boundary points of a John domain and unions of convex sets, J. Math. Soc. Japan, 58, 1 (2006), 247-274, MR2204573 (2006k:31008), preprint , ARTICLE

  6. H. Aikawa and N. Shanmugalingam, Hölder estimates of p-harmonic extension operators, J. Differential Equations, 220, 1 (2006), 18-45, MR2182078, preprint , ARTICLE

  7. H. Aikawa, Characterization of a uniform domain by the boundary Harnack principle, in Harmonic analysis and its applications, Yokohama Publ., Yokohama (2006), 1-17, MR2213453 (2006m:31004)

  8. H. Aikawa and N. Shanmugalingam, Carleson-type estimates for p-harmonic functions and the conformal Martin boundary of John domains in metric measure spaces, Michigan Math. J., 53, 1 (2005), 165-188, MR2125540 (2005k:31029), preprint , ARTICLE

  9. H. Aikawa and T. Lundh, The 3G inequality for a uniformly John domain, Kodai Math. J., 28, 2 (2005), 209-219, MR2153910 (2006b:31007), preprint , ARTICLE

  10. H. Aikawa, Potential-theoretic characterizations of nonsmooth domains, Bull. London Math. Soc., 36, 4 (2004), 469-482, MR2069009 (2005e:31005), preprint , ARTICLE

  11. H. Aikawa, Fatou and Littlewood theorems for Poisson integrals with respect to non-integrable kernels, Complex Var. Theory Appl., 49, 7-9 (2004), 511-528, MR2088043 (2005f:31009), preprint , ARTICLE

  12. H. Aikawa, Positive harmonic functions of finite order in a Denjoy type domain, Proc. Amer. Math. Soc., 131, 12 (2003), 3873-3881 (electronic), MR1999936 (2004k:31004), preprint , ARTICLE

  13. H. Aikawa, T. Lundh, and T. Mizutani, Martin boundary of a fractal domain, Potential Anal., 18, 4 (2003), 311-357, MR1953266 (2004a:31002), preprint , ARTICLE

  14. H. Aikawa, Hölder continuity of the Dirichlet solution for a general domain, Bull. London Math. Soc., 34, 6 (2002), 691-702, MR1924196 (2003f:31007), preprint , ARTICLE

  15. H. Aikawa, Boundary Harnack principle and Martin boundary for a uniform domain, J. Math. Soc. Japan, 53, 1 (2001), 119-145, MR1800526 (2001m:31007), preprint , ARTICLE

  16. H. Aikawa, Integrability of superharmonic functions in a John domain, Proc. Amer. Math. Soc., 128, 1 (2000), 195-201, MR1622765 (2000c:31002), preprint , ARTICLE

  17. H. Aikawa and S. J. Gardiner, Evaluation of superharmonic functions using limits along lines, Bull. London Math. Soc., 32, 2 (2000), 209-213, MR1734186 (2001b:31004), preprint , ARTICLE

  18. H. Aikawa and M. Ohtsuka, Extremal length of vector measures, Ann. Acad. Sci. Fenn. Math., 24, 1 (1999), 61-88, MR1677985 (2000i:31001), preprint

  19. H. Aikawa, Norm estimate of Green operator, perturbation of Green function and integrability of superharmonic functions, Math. Ann., 312, 2 (1998), 289-318, MR1671780 (99m:35042), preprint , ARTICLE

  20. H. Aikawa, Generalized Cranston-McConnell inequalities for discontinuous superharmonic functions, Potential Anal., 8, 2 (1998), 127-135, MR1618430 (99g:31001), preprint , ARTICLE

  21. H. Aikawa, Densities with the mean value property for harmonic functions in a Lipschitz domain, Proc. Amer. Math. Soc., 125, 1 (1997), 229-234, MR1363444 (97c:31006), preprint , ARTICLE

  22. H. Aikawa, Sets of determination for harmonic functions in an NTA domain, J. Math. Soc. Japan, 48, 2 (1996), 299-315, MR1376083 (97f:31005), preprint , ARTICLE

  23. H. Aikawa and A. A. Borichev, Quasiadditivity and measure property of capacity and the tangential boundary behavior of harmonic functions, Trans. Amer. Math. Soc., 348, 3 (1996), 1013-1030, MR1340166 (96h:31004), preprint , ARTICLE

  24. H. Aikawa and T. Lundh, On boundary layers, Ark. Mat., 34, 1 (1996), 1-19, MR1396620 (97j:31004), preprint , ARTICLE

  25. H. Aikawa and M. Murata, Generalized Cranston-McConnell inequalities and Martin boundaries of unbounded domains, J. Anal. Math., 69 (1996), 137-152, MR1428098 (98f:31016), preprint , ARTICLE

  26. H. Aikawa, Bessel capacity, Hausdorff content and the tangential boundary behavior of harmonic functions, Hiroshima Math. J., 26, 2 (1996), 363-384, MR1400547 (97j:31005), preprint , ARTICLE

  27. H. Aikawa, On the upper bounds of Green potentials, Hiroshima Math. J., 24, 3 (1994), 607-612, MR1309143 (95m:31001), preprint , ARTICLE

  28. H. Aikawa, Integrability of superharmonic functions and subharmonic functions, Proc. Amer. Math. Soc., 120, 1 (1994), 109-117, MR1169019 (94b:31003), preprint , ARTICLE

  29. H. Aikawa, Quasiadditivity of capacity and minimal thinness, Ann. Acad. Sci. Fenn. Ser. A I Math., 18, 1 (1993), 65-75, MR1207895 (94d:31004), preprint

  30. H. Aikawa, Thin sets at the boundary, Proc. London Math. Soc. (3), 65, 2 (1992), 357-382, MR1168192 (93g:31012), preprint , ARTICLE

  31. H. Aikawa, Infinite order Sobolev spaces, analytic continuation and polynomial expansions, Complex Variables Theory Appl., 18, 3-4 (1992), 253-266, MR1157933 (93c:46049), preprint

  32. H. Aikawa, Quasiadditivity of Riesz capacity, Math. Scand., 69, 1 (1991), 15-30, MR1143471 (93d:31007), preprint

  33. H. Aikawa, N. Hayashi, and S. Saitoh, Isometrical identities for the Bergman and the Szeg\H o spaces on a sector, J. Math. Soc. Japan, 43, 1 (1991), 195-201, MR1082430 (91m:30060)

  34. H. Aikawa and N. Hayashi, Holomorphic solutions of semilinear heat equations, Complex Variables Theory Appl., 16, 2-3 (1991), 115-125, MR1099906 (92e:35084), preprint

  35. H. Aikawa, Harmonic functions and Green potentials having no tangential limits, J. London Math. Soc. (2), 43, 1 (1991), 125-136, MR1099092 (92b:31005), preprint , ARTICLE

  36. H. Aikawa, N. Hayashi, I. Onda, and S. Saitoh, Analytical extensions of the members of the Bergman and Szeg\H o spaces on some tube domains, Arch. Math. (Basel), 56, 4 (1991), 362-369, MR1094423 (91m:32004), ARTICLE

  37. H. Aikawa, Harmonic functions having no tangential limits, Proc. Amer. Math. Soc., 108, 2 (1990), 457-464, MR990410 (90h:31003), ARTICLE

  38. H. Aikawa, Comparison of L\sp p-capacity and Hausdorff measure, Complex Variables Theory Appl., 15, 3 (1990), 223-232, MR1074064 (91i:31005)

  39. H. Aikawa, N. Hayashi, and S. Saitoh, The Bergman space on a sector and the heat equation, Complex Variables Theory Appl., 15, 1 (1990), 27-36, MR1055936 (91k:30019), ARTICLE

  40. H. Aikawa, On weighted Beppo Levi functions--integral representations and behavior at infinity, Analysis, 9, 4 (1989), 323-346, MR1032579 (91e:46037), preprint

  41. H. Aikawa, On subharmonic functions in strips, Ann. Acad. Sci. Fenn. Ser. A I Math., 12, 1 (1987), 119-134, MR877585 (88a:31005)

  42. H. Aikawa, Tangential boundary behavior of Green potentials and contractive properties of L\sp p-capacities, Tokyo J. Math., 9, 1 (1986), 223-245, MR852983 (87j:31007)

  43. H. Aikawa, On the Martin boundary of Lipschitz strips, J. Math. Soc. Japan, 38, 3 (1986), 527-541, MR845719 (88f:31013), ARTICLE

  44. H. Aikawa, On the minimal thinness in a Lipschitz domain, Analysis, 5, 4 (1985), 347-382, MR816586 (87h:31010)

  45. H. Aikawa, On the behavior at infinity of nonnegative superharmonic functions in a half space, Hiroshima Math. J., 11, 2 (1981), 425-441, MR620547 (82g:31003), ARTICLE

Proceedings

  1. H. Aikawa, Characterization of a uniform domain by the boundary Harnack principle, in Harmonic analysis and its applications, Yokohama Publ., Yokohama (2006), 1-17, MR2213453 (2006m:31004)

  2. H. Aikawa, Norm estimate of the Green operator and its application, in Complex analysis and differential equations (Uppsala, 1997), Vol. 64 of Acta Univ. Upsaliensis Skr. Uppsala Univ. C Organ. Hist., Uppsala Univ., Uppsala (1999), 37-50, MR1758913 (2001b:31003)

  3. H. Aikawa and A. A. Borichev, Quasiadditivity and measure property of capacity and the tangential boundary behavior of harmonic functions, in Potential theory--ICPT 94 (Kouty, 1994), de Gruyter, Berlin (1996), 219-227, MR1404708 (97e:31002), preprint

  4. H. Aikawa, On weighted Beppo Levi function, in Potential theory (Prague, 1987), Plenum, New York (1988), 1-6, MR986271 (90e:46007)

Memoirs

  1. H. Aikawa, Dirichlet problem in an exterior domain with potential in a weighted Lebesgue class, Mem. Fac. Sci. Eng. Shimane Univ. Ser. B Math. Sci., 32 (1999), 9-23, MR1688380 (2000d:35036), preprint

  2. H. Aikawa, Semibounded perturbation of Green function in an NTA domain, Mem. Fac. Sci. Eng. Shimane Univ. Ser. B Math. Sci., 31 (1998), 1-7, MR1618984 (99c:31007), preprint

  3. H. Aikawa, Capacity and Hausdorff content of certain enlarged sets, Mem. Fac. Sci. Eng. Shimane Univ. Ser. B Math. Sci., 30 (1997), 1-21, MR1460405 (99b:31004), preprint