Geodesic
$\alpha$-Subharmonic functions
Contemporary Mathematics. Fundamental Directions, Science — Technology — Education — Mathematics — Medicine, Tome 67 (2021) no. 4, pp. 620-633.

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

In this paper, we study the class of $\alpha$-subharmonic functions. A number of important properties of $\alpha$-subharmonic functions are proved, and an equivalent, more convenient definition of $\alpha$-subharmonicity is given. The geometric structure of removable singularities for some classes of $\alpha$-subharmonic functions is also described. 
@article{CMFD_2021_67_4_a1,
     author = {B. I. Abdullaev and S. A. Imomkulov and R. A. Sharipov},
     title = {$\alpha${-Subharmonic} functions},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {620--633},
     publisher = {mathdoc},
     volume = {67},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2021_67_4_a1/}
}
TY  - JOUR
AU  - B. I. Abdullaev
AU  - S. A. Imomkulov
AU  - R. A. Sharipov
TI  - $\alpha$-Subharmonic functions
JO  - Contemporary Mathematics. Fundamental Directions
PY  - 2021
SP  - 620
EP  - 633
VL  - 67
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMFD_2021_67_4_a1/
LA  - ru
ID  - CMFD_2021_67_4_a1
ER  - 
%0 Journal Article
%A B. I. Abdullaev
%A S. A. Imomkulov
%A R. A. Sharipov
%T $\alpha$-Subharmonic functions
%J Contemporary Mathematics. Fundamental Directions
%D 2021
%P 620-633
%V 67
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMFD_2021_67_4_a1/
%G ru
%F CMFD_2021_67_4_a1
B. I. Abdullaev; S. A. Imomkulov; R. A. Sharipov. $\alpha$-Subharmonic functions. Contemporary Mathematics. Fundamental Directions, Science — Technology — Education — Mathematics — Medicine, Tome 67 (2021) no. 4, pp. 620-633. http://geodesic.mathdoc.fr/item/CMFD_2021_67_4_a1/

[1] Abdullaev B., Imomkulov S., “Ustranimye osobennosti subgarmonicheskikh funktsii iz klassa $L_{p}$ i $L_{p}^{1}$”, Uzb. mat. zh., 1997, no. 4, 10–14 | Zbl

[2] Abdullaev B., Sadullaev A., “Teoriya potentsialov v klasse $m$-cubgarmonicheskikh funktsii”, Tr. MIAN, 279, 2012, 166–192 | MR | Zbl

[3] Abdullaev B. I., Yarmetov Zh. R., “Ob osobykh mnozhestvakh subreshenii ellipticheskikh operatorov”, Vestn. Kras. GU, 2006, no. 9, 74–80

[4] Alimov Sh. A., “Drobnye stepeni ellipticheskikh operatorov i izomorfizm klassov differentsiruemykh funktsii”, Diff. uravn., 8:9 (1972), 1609–1626 | Zbl

[5] Bers L., Dzhon F., Shekhter M., Uravneniya s chastnymi proizvodnymi, Mir, M., 1966

[6] Vaisova M., “Teoriya potentsiala v klasse $\alpha$-subgarmonicheskikh funktsii”, Uzb. mat. zh., 2016, no. 3, 46–52 | MR

[7] Vaisova M., “Emkost v klasse $\alpha$-subgarmonicheskikh funktsii i ee svoistva”, Ilm sarchashmalari, 2018, no. 6, 8–13

[8] Dolzhenko E. P., “Ob osobykh tochkakh nepreryvnykh garmonicheskikh funktsii”, Izv. AN CCSR, 28:6 (1964), 1251–1270 | Zbl

[9] Karleson L., Izbrannye problemy teorii isklyuchitelnykh mnozhestv, Mir, M., 1971

[10] Landkof N. S., Osnovy sovremennoi teorii potentsiala, Nauka, M., 1966

[11] Mazya V. G., “Klassy mnozhestv i mer, svyazannye s teoremami vlozheniya”, Teoremy vlozheniya i ikh prilozheniya, Nauka, M., 1970, 142–159

[12] Mazya V. G., Khavin V. P., “Nelineinaya teoriya potentsiala”, Usp. mat. nauk, 27:6 (1972), 67–138 | MR | Zbl

[13] Melnikov M. S., Sinanyan S. O., “Voprosy teorii priblizhenii funktsii odnogo kompleksnogo peremennogo”, Itogi nauki i tekhn. Sovrem. probl. mat., 4, 1975, 143–250 | Zbl

[14] Miranda K., Uravneniya s chastnymi proizvodnymi ellipticheskogo tipa, IL, M., 1957

[15] Sadullaev A., “Plyurisubgarmonicheskie funktsii”, Sovrem. probl. mat. Fundam. napravl., 8, 1985, 65–111 | MR

[16] Sadullaev A., Abdullaev B., Sharipov R., “Ustranimye osobennosti ogranichennykh sverkhu $m-sh$ funktsii”, Uzb. mat. zh., 2016, no. 3, 118–124

[17] Sadullaev A., Yarmetov Zh. R., “Ustranimye osobennosti subgarmonicheskikh funktsii klassa $Lip_{\alpha}$”, Mat. sb., 186:1 (1995), 131–148 | MR | Zbl

[18] Kheiman U., Kennedi P., Subgarmonicheskie funktsii, Mir, M., 1980

[19] Cegrell U., “Sur les ensembles singuliers impropes des plurisubharmonic”, C.R. Math. Acad. Sci. Paris, 281 (1975), 905–908 | Zbl

[20] Chirka E. M., “On the removal of subharmonic singularities of plurisubharmonic functions”, Ann. Polon. Math., 80 (2003), 113–116 | DOI | MR | Zbl

[21] Demailly J.-P., Complex analytic and differential geometry, Universite de Grenoble I, Saint-Martin d'Héres, 1997

[22] Harve R., Polking J. C., “A notion of capacity which characterizes removable singularites”, Trans. Am. Math. Soc., 169 (1968), 183–195 | DOI

[23] Littman W., Stampasshia G., Weinberger H. F., “Regular points for elliptic equations with discontinuous coefficients”, Ann. Sc. Norm. Super. Pisa Cl. Sci. (3), 17 (1963), 43–77 | Zbl

[24] Riihentaus J., “A removability results for holomorphic functions of several complex variables”, J. Basic Appl. Sci., 12 (2016), 50–52 | DOI

[25] Shapiro V. L., “Subharmonic functions and Hausdorff measure”, J. Differ. Equ., 27:1 (1978), 28–45 | DOI | Zbl