Geodesic
Various Types of Convergence of Sequences of Subharmonic Functions
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 11 (2015) no. 1, pp. 63-74 
Van Quynh Nguyen. Various Types of Convergence of Sequences of Subharmonic Functions. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 11 (2015) no. 1, pp. 63-74. http://geodesic.mathdoc.fr/item/JMAG_2015_11_1_a3/
@article{JMAG_2015_11_1_a3,
     author = {Van Quynh Nguyen},
     title = {Various {Types} of {Convergence} of {Sequences} of {Subharmonic} {Functions}},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {63--74},
     year = {2015},
     volume = {11},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2015_11_1_a3/}
}
TY  - JOUR
AU  - Van Quynh Nguyen
TI  - Various Types of Convergence of Sequences of Subharmonic Functions
JO  - Žurnal matematičeskoj fiziki, analiza, geometrii
PY  - 2015
SP  - 63
EP  - 74
VL  - 11
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/JMAG_2015_11_1_a3/
LA  - en
ID  - JMAG_2015_11_1_a3
ER  - 
%0 Journal Article
%A Van Quynh Nguyen
%T Various Types of Convergence of Sequences of Subharmonic Functions
%J Žurnal matematičeskoj fiziki, analiza, geometrii
%D 2015
%P 63-74
%V 11
%N 1
%U http://geodesic.mathdoc.fr/item/JMAG_2015_11_1_a3/
%G en
%F JMAG_2015_11_1_a3

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $\upsilon_n(x)$ be a sequence of subharmonic functions in a domain $G\subset\mathbb{R}^m$. The conditions under which the convergence of $\upsilon_n(x)$, as a sequence of generalized functions, implies its convergence in the Lebesgue spaces $L_p(\gamma)$ are studied. The results similar to ours have been obtained earlier by Hörmander and also by Ghisin and Chouigui. Hörmander investigated the case where the measure $\gamma$ is some restriction of the $m$-dimensional Lebesgue measure. Grishin and Chouigui considered the case $m=2$. In this paper we consider the case $m>2$ and general measures $\gamma$.

[1] L. Hörmander, The Analysis of Linear Partial Differential Operators, v. II, Differential Operators with Constant Coefficients, Springer-Verlag, Berlin–Heidelberg–New York–Tokyo, 1983

[2] A. F. Grishin, A. Chouigui, “Various Types of Convergence of Sequences of $\delta$-subharmonic Functions”, Math. Sb., 199 (2008), 27–48 (Russian) | DOI | MR | Zbl

[3] N. S. Landkof, Foundations of Modern Potential Theory, Nauka, M., 1966 (Russian) | MR | Zbl

[4] N. Burbaki, Elements of Mathematics. Integration, Nauka, M., 1977 (Russian) | MR

[5] L. Hörmander, The Analysis of Linear Partial Differential Operators, v. I, Distribution Theory and Fourier Analysis, Springer-Verlag, Berlin–Heidelberg–New York–Tokyo, 1983 | MR

[6] Nguyen Van Quynh, “About one Property of the Function $||x-y||^{2-m}$”, Visnyk Kharkiv. Univ., Ser. Mat. Prykl. Mat. Mekh., 2013, no. 1062, 50–56 (Russian)