Comparison theorems for Banach spaces of solutions of Δu=Pu on Riemann surfaces

Takeyoshi SATO

doi:10.2969/jmsj/03120281

Takeyoshi SATO

著者情報

ジャーナルフリー

1979 年 31 巻 2 号 p. 281-316

DOI https://doi.org/10.2969/jmsj/03120281

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Published: 1979 Received: 1977/08/26 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 論文タイトル訂正内容: Wrong : Comparison theorems for Banach spaces of solutions of Δu=Pu on Riemann surfaces
Right : Comparison theorems for Banach spaces of solutions of Δu=Pu on Riemann surfaces

訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) M. Glasner Comparison theorems for bounded solutions of Δu=Pu, Trans. Amer. Math. Soc., 202 (1975), 173-179.
2) L.L. Helms Introduction to potential theory, Wiley-Interscience, New-York, 1969.
3) A. Lahtinen On the solutions of Δu=Pu for acceptable densities on open Riemann surfaces, Ann. Acad. Sci. Fenn. Ser. AI, No.515 (1972).
4) A. Lahtinen On the equation Δu=Pu and the classification of acceptable densities on Riemann surfaces, Ann. Acad. Sci. Fenn. Ser. AI, No. 533 (1973).
5) L. Myrberg Über die Integration der Differentialgleichung Δu=c(P)u auf offenen Riemannschen Flächen, Math. Scad., 2 (1954), 142-152.
6) L. Myrberg Über die Existenz der Greenschen Funktion der Gleichung Δu=c(P)u auf Riemannschen Flächen, Ann. Acad. Sci. Fenn. Ser. AI, No. 170 (1954).
7) L. Myrberg Über subelliptische Funktionen, Ann. Acad. Sci. Fenn. Ser. AI, No. 290 (1960).
8) L. Lumer-Naim H^p-spaces of harmonic functions, Ann. Inst. Fourier (Grenoble), 17 (1967), 425-469.
9) M. Nakai The space of bounded solutions of the equation Δu=Pu on a Riemann surface, Proc. Japan Acad., 36 (1960), 267-272.
10) M. Nakai The space of non-negative solutions of the equation Δu=Pu on a Riemann surface, Kodai Math. Sem. Rep., 12 (1960), 151-178.
11) M. Nakai Order comparisons on canonical isomorphisms, Nagoya Math. J., 50 (1973), 67-87.
12) M. Nakai Banach spaces of bounded solutions of Δu=Pu(P_??_0) on hyperbolic Riemann surfaces, Nagoya Math. J., 53 (1974), 141-155.
13) M. Parreau Sur les moyennes des fonctions harmoniques et analytiques et la classification des surfaces de Riemann, Ann. Inst. Fourier (Grenoble), 3 (1951), 103-197.
14) B. Rodin and L. Sario Principal functions, D. Van Nostrand Company, INC., Princeton, 1968.
15) H.L. Royden The equation Δu=Pu and the classifications of open Riemann surfaces, Ann. Acad. Fenn. Ser. AI, No. 271 (1959).
16) L. Sario and M. Nakai Classification theory of Riemann surfaces, Springer-Verlag, Berlin, 1970.
17) J.L. Schiff Isomorphisms between harmonic and P-harmonic Hardy spaces on Riemann surfaces, Pacific J. Math., 62 (1976), 551-560.

Right : [1] M. Glasner Comparison theorems for bounded solutions of Δu=Pu, Trans. Amer. Math. Soc., 202 (1975), 173-179.
[1] L. L. Helms Introduction to potential theory, Wiley-Interscience, New-York, 1969.
[1] A. Lahtinen On the solutions of Δu=Pu for acceptable densities on open Riemann surfaces, Ann. Acad. Sci. Fenn. Ser. AI, No. 515 (1972).
[2] A. Lahtinen On the equation Δu=Pu and the classification of acceptable densities on Riemann surfaces, Ann. Acad. Sci. Fenn. Ser. AI, No. 533 (1973).
[1] L. Myrberg Über die Integration der Differentialgleichung Δu=c(P)u auf offenen Riemannschen Flächen, Math. Scad., 2 (1954), 142-152.
[2] L. Myrberg Über die Existenz der Greenschen Funktion der Gleichung Δu=c(P)u auf Riemannschen Flächen, Ann. Acad. Sci. Fenn. Ser. AI, No. 170 (1954).
[3] L. Myrberg Über subelliptische Funktionen, Ann. Acad. Sci. Fenn. Ser. AI, No. 290 (1960).
[1] L. Lumer-Naim H^p-spaces of harmonic functions, Ann. Inst. Fourier (Grenoble), 17 (1967), 425-469.
[1] M. Nakai The space of bounded solutions of the equation Δu=Pu on a Riemann surface, Proc. Japan Acad., 36 (1960), 267-272.
[2] M. Nakai The space of non-negative solutions of the equation Δu=Pu on a Riemann surface, Kodai Math. Sem. Rep., 12 (1960), 151-178.
[3] M. Nakai Order comparisons on canonical isomorphisms, Nagoya Math. J., 50 (1973), 67-87.
[4] M. Nakai Banach spaces of bounded solutions of Δu=Pu(P≥0) on hyperbolic Riemann surfaces, Nagoya Math. J., 53 (1974), 141-155.
[1] M. Parreau Sur les moyennes des fonctions harmoniques et analytiques et la classification des surfaces de Riemann, Ann. Inst. Fourier (Grenoble), 3 (1951), 103-197.
[1] B. Rodin and L. Sario Principal functions, D. Van Nostrand Company, INC., Princeton, 1968.
[1] H. L. Royden The equation Δu=Pu and the classifications of open Riemann surfaces, Ann. Acad. Fenn. Ser. AI, No. 271 (1959).
[1] L. Sario and M. Nakai Classification theory of Riemann surfaces, Springer-Verlag, Berlin, 1970.
[1] J. L. Schiff Isomorphisms between harmonic and P-harmonic Hardy spaces on Riemann surfaces, Pacific J. Math., 62 (1976), 551-560.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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