Capacities of generalized condensers with $A_1$-Muckenhoupt weight
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 1, pp. 164-186.

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

We prove the relations (related to $A_1$-Muckenhoupt weight) between two capacities of a generalized condenser and the moduli of vector measures on the curve configuration.
Keywords: capacity of condenser, Muckenhoupt weight, modulus of vector measures.
@article{SEMR_2022_19_1_a30,
     author = {Yu. V. Dymchenko and V. A. Shlyk},
     title = {Capacities of generalized condensers with $A_1${-Muckenhoupt} weight},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {164--186},
     publisher = {mathdoc},
     volume = {19},
     number = {1},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2022_19_1_a30/}
}
TY  - JOUR
AU  - Yu. V. Dymchenko
AU  - V. A. Shlyk
TI  - Capacities of generalized condensers with $A_1$-Muckenhoupt weight
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2022
SP  - 164
EP  - 186
VL  - 19
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2022_19_1_a30/
LA  - en
ID  - SEMR_2022_19_1_a30
ER  - 
%0 Journal Article
%A Yu. V. Dymchenko
%A V. A. Shlyk
%T Capacities of generalized condensers with $A_1$-Muckenhoupt weight
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2022
%P 164-186
%V 19
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2022_19_1_a30/
%G en
%F SEMR_2022_19_1_a30
Yu. V. Dymchenko; V. A. Shlyk. Capacities of generalized condensers with $A_1$-Muckenhoupt weight. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 1, pp. 164-186. http://geodesic.mathdoc.fr/item/SEMR_2022_19_1_a30/

[1] P.S. Aleksandrov, Lektsii po analiticheskoy geometrii, Nauka, M., 1968 | MR

[2] H. Aikawa, M. Ohtsuka, “Extremal lenth of vector measures”, Ann. Acad. Sci. Fenn., Math., 24:1 (1999), 61–88 | MR | Zbl

[3] V.V. Aseev, “On a modulus property”, Sov. Math., Dokl., 12 (1971), 1409–1411 | MR | Zbl

[4] V.I. Bogachev, O.G. Smolyanov, Real and functional analysis, Springer, Cham, 2020 | MR | Zbl

[5] V.N. Dubinin, “Asymptotics for the capacity of a condenser with variable potential levels”, Sib. Math. J., 61:4 (2020), 626–631 | DOI | MR | Zbl

[6] Y.V. Dymchenko, “Equality of the capacity and module of a condenser on a surface”, J. Math. Sci., New York, 118:1 (2003), 4795–4807 | DOI | MR | Zbl

[7] Y.V. Dymchenko, V.A. Shlyk, “On a problem of Dubinin for the capacity of a condenser with a finite number of plates”, Math. Notes, 103:6 (2018), 901–910 | DOI | MR | Zbl

[8] B. Fuglede, “Extremal length and functional completion”, Acta Math., 98 (1957), 171–219 | DOI | MR | Zbl

[9] J. Hesse, “A $p$-extremal length and $p$-capacity equality”, Ark. Mat., 13 (1975), 131–144 | DOI | MR | Zbl

[10] O. Martio, V. Ryazanov, U. Srebro, E. Yakubov, Moduli in modern mapping theory, Springer, New York, 2009 | MR | Zbl

[11] V.G. Maz'ya, Sobolev spaces, Springer, Berlin etc, 1985 | MR | Zbl

[12] B. Muckenhoupt, “Weighted norm unequalities for the Hardy maximal function”, Trans. Am. Math. Soc., 165 (1972), 207–226 | DOI | MR | Zbl

[13] M. Ohtsuka, “Extremal length and precise functions. With a preface by Fumi-Yuki Maeda”, GAKUTO International Series. Mathematical Sciences and Applications, 19, Gakkōtosho, Tokyo, 2003 | MR | Zbl

[14] W. Rudin, Real and complex analysis, 3rd Ed., McGraw-Hill, New York, 1987 | MR | Zbl

[15] I.M. Tarasova, V.A. Shlyk, “Weighted Sobolev spaces, capacities and exceptional sets”, Sib. Èlectron. Mat. Izv., 17 (2020), 1552–1570 | DOI | MR | Zbl

[16] B.O. Turesson, Nonlinear potential theory and weighted Sobolev spaces, Springer, Berlin, 2000 | MR | Zbl