Geodesic
Modules of families of vector measures on a Riemann surface
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 33, Tome 458 (2017), pp. 31-41 
Yu. V. Dymchenko; V. A. Shlyk. Modules of families of vector measures on a Riemann surface. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 33, Tome 458 (2017), pp. 31-41. http://geodesic.mathdoc.fr/item/ZNSL_2017_458_a3/
@article{ZNSL_2017_458_a3,
     author = {Yu. V. Dymchenko and V. A. Shlyk},
     title = {Modules of families of vector measures on {a~Riemann} surface},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {31--41},
     year = {2017},
     volume = {458},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_458_a3/}
}
TY  - JOUR
AU  - Yu. V. Dymchenko
AU  - V. A. Shlyk
TI  - Modules of families of vector measures on a Riemann surface
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2017
SP  - 31
EP  - 41
VL  - 458
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2017_458_a3/
LA  - ru
ID  - ZNSL_2017_458_a3
ER  - 
%0 Journal Article
%A Yu. V. Dymchenko
%A V. A. Shlyk
%T Modules of families of vector measures on a Riemann surface
%J Zapiski Nauchnykh Seminarov POMI
%D 2017
%P 31-41
%V 458
%U http://geodesic.mathdoc.fr/item/ZNSL_2017_458_a3/
%G ru
%F ZNSL_2017_458_a3

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We consider a Riemann surface in the broad sense of the term in the Hurwitz–Courant terminology and an open set with a compact closure on this surface. In this paper, it is established that a family of vector measures can be associated with a condenser on a given open set, following the Aikawa–Ohtsuka, whose modules are calculated directly with the help of a weighted capacity (with Muckenhoupt weight) of the given condenser.

[1] A. Gurvits, R. Kurant, Teoriya funktsii, Nauka, 1968 | MR

[2] K. Iosida, Funktsionalnyi analiz, Mir, M., 1967 | MR

[3] D. Milman, “O nekotorykh priznakakh regulyarnosti prostranstv tipa (V)”, DAN SSSR, 20 (1938), 243–246 | Zbl

[4] P. A. Pugach, V. A. Shlyk, “Vesovye moduli i emkosti na rimanovoi poverkhnosti”, Zap. nauchn. semin. POMI, 458, 2017, 164–217

[5] S. Stoilov, Lektsii o topologicheskikh printsipakh teorii analiticheskikh funktsii, Nauka, 1964 | MR

[6] D. Adams, L. Hedberg, Function Spaces and Potential Theory, Springer-Verlag, 1996 | MR

[7] H. Aikawa, M. Ohtsuka, “Extremal length of vector measures”, Ann. Acad. Sci. Fenn. Ser. A, 24 (1999), 61–88 | MR | Zbl

[8] K. Fan, “Minimax Theorems”, Proc. Nat. Acad. Sci. USA, 39:1 (1953), 42–47 | DOI | MR | Zbl

[9] M. Ohtsuka, Extremal length and precise functions, GAKUTO international series, Gakkōtosho, 2003 | MR | Zbl

[10] P. Pugach, V. Shlyk, “Moduli, capacity, BV-functions on the Riemann surfaces”, Lobachevskii J. Math., 38:2 (2017), 338–351 | DOI | MR | Zbl