The local uniform convergence of positive harmonic function sequence
Vol. 131 No. 1D (2022), Original Article
Vol. 131 No. 1D (2022)

The local uniform convergence of positive harmonic function sequence

Original Article
https://doi.org/10.26459/hueunijns.v131i1D.6663
Published 2023-05-09
Do Dang Thinh*
Faculty of Mathematics, University of Science and Education, The University of Da Nang, 459 Ton Duc Thang St., Lien Chieu District, Da Nang, Vietnam
Tran Le Dieu Linh
Faculty of Mathematics, University of Science and Education, The University of Da Nang, 459 Ton Duc Thang St., Lien Chieu District, Da Nang, Vietnam
Hoang Nhat Quy
Faculty of Mathematics, University of Science and Education, The University of Da Nang, 459 Ton Duc Thang St., Lien Chieu District, Da Nang, Vietnam
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Keywords

harmonic function
harnack distance
local uniform convergence harmonic function
Harnack distance
local uniform convergence

How to Cite

1.
Do DT, Tran LDL, Hoang NQ. The local uniform convergence of positive harmonic function sequence. hueuni-jns [Internet]. 2023May9 [cited 2024Dec.5];131(1D):61-5. Available from: https://jos.hueuni.edu.vn/index.php/hujos-ns/article/view/6663
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Abstract

The Harnack distance on space  and its conformal invariance were constructed and studied by Herron. In this paper, we obtain the Harnack distance on domains  in . Then, we use this concept to investigate some properties of the positive harmonic function class. These results are obtained in the complex plane, so it is advantageous to take some tools of the complex analysis. The main result of this paper is the property of the local uniform convergence of the positive harmonic sequences on a domain in the complex plane.

https://doi.org/10.26459/hueunijns.v131i1D.6663
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References

  1. Axler S, Bourdon P, Ramey W. Harmonic function theory. New York: Springer – Verlag; 2001. 264 p.
  2. Klimek M. Pluripotential Theory. Oxford: Clarendon Press; 1991.
  3. Helms LL. Introduction to potential theory. New York: John Wiley and Sons; 1969.
  4. Herron DA. The harnack and other conformally invariant metrics. Kodai Mathematical Journal. 1987;10(1):9-19.
  5. Hiep PH. Singularities of plurisubharmonic functions. Pub Hou Sci and Tec; 2016.
  6. Quy HN. The topology on the space δE_χ. Univ Iagel Acta Math. 2014;51:61-73.
  7. Hung VV, Quy HN. The m-Hessian Operator on Some Weighted Energy Classes of Delta m-Subharmonic Functions. Results in Mathematics. 2020;75(3):112.
  8. Khue NV, Hai LM. Functions of One complex variable. Hanoi: Hanoi Vietnam National University Press; 1997.
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