Geodesic
Cylindrical Carleman's formula of subharmonic functions and its application
Qiao, Lei 1
1 School of Mathematics and Information Science, Henan University of Economics and Law, Zhengzhou 450046, China
Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 8, p. 947-952.

Voir la notice de l'article provenant de la source International Scientific Research Publications

Our aim in this paper is to prove the cylindrical Carleman's formula for subharmonic functions in a truncated cylinder. As an application, we prove that if the positive part of a harmonic function in a cylinder satisfies a slowly growing condition, then its negative part can also be dominated by a similar slowly growing condition, which improves some classical results about harmonic functions in a cylinder.
DOI : 10.22436/jnsa.011.08.01
Classification : 31B05, 31B10, 35J05, 35J10, 35J40
Keywords: Cylindrical Carleman's formula, subharmonic function, cylinder

Qiao, Lei  1

1 School of Mathematics and Information Science, Henan University of Economics and Law, Zhengzhou 450046, China 
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Qiao, Lei . Cylindrical Carleman's formula of subharmonic functions and its application. Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 8, p. 947-952. doi : 10.22436/jnsa.011.08.01. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.011.08.01/

[1] Armitage, D. H. A Nevanlinna theorem for superharmonic functions in half-spaces, with applications, J. London Math. Soc., Volume 23 (1981), pp. 137-157 | DOI

[2] Gilbarg, D.; Trudinger, N. S. Elliptic partial differential equations of second order, Grundlehren der Mathematischen Wissenschaften, Springer-Verlag, Berlin-New York, 1977 | DOI

[3] Kuran, Ü. Harmonic majorizations in half-balls and half-spaces, Proc. London Math. Soc., Volume 21 (1970), pp. 614-636 | DOI

[4] B. Y. Levin Entire and subharmonic functions, Adv. Soviet Math., Amer. Math. Soc., Providence, RI, 1992

[5] Miyamoto, I. Harmonic functions in a cylinder which vanish on the boundary, Japan. J. Math., Volume 22 (1996), pp. 241-255 | DOI

[6] Miyamoto, I.; H. Yoshida Harmonic functions in a cylinder with normal derivatives vanishing on the boundary, Ann. Polon. Math., Volume 74 (2000), pp. 229-235 | DOI

[7] Miyamoto, I.; Yoshida, H. On a covering property of minimally thin sets at infinity in a cylinder, Math. Montisnigri, Volume 20/21 (2007/08), pp. 35-54

[8] Qiao, L. Asymptotic behavior of Poisson integrals in a cylinder and its application to the representation of harmonic functions, Bull. Sci. Math., Volume 144 (2018), pp. 39-54 | DOI

[9] Rashkovskiı, A. Y.; Ronkin, L. I. Subharmonic functions of finite order in a cone. III., Functions of completely regular growth, J. Math. Sci., Volume 77 (1995), pp. 2929-2940

[10] Ronkin, L. I. Functions of completely regular growth , Kluwer Academic Publishers Group , Dordrecht, 1992 | DOI

[11] Rozenblyum, G. V.; Solomyak, M. Z.; Shubin, M. A. Spectral theory of differential operators, Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1989

[12] Yoshida, H. Harmonic majorization of a subharmonic function on a cone or on a cylinder , Pacific J. Math., Volume 148 (1991), pp. 369-395 | Zbl

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