Yu. V. Dymchenko, V. A. Shlyk, “Capacities of generalized condensers with <nobr>$A_1$</nobr>-Muckenhoupt weight”, Sib. Èlektron. Mat. Izv., 2022, Volume 19, Issue 1,Pages <nobr>164–186</nobr>

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JOURNALS // Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports] // Archive

Sib. Èlektron. Mat. Izv., 2022 Volume 19, Issue 1, Pages 164–186 (Mi semr1491)

Real, complex and functional analysis

Capacities of generalized condensers with $A_1$-Muckenhoupt weight

Yu. V. Dymchenko^abc, V. A. Shlyk^dc

^a Maritime State University, 50a, Verkhneportovaya str., Vladivostok, 690059, Russia
^b Institute of Applied Mathematics, Vladivostok Branch of the RAS 7, Radio str., Vladivostok, 690041, Russia
^c Far Eastern Federal University, Far Eastern Center for Research and Education in Mathematics, 10, Ajax Bay, Vladivostok, 690922, Russia
^d Vladivostok Branch of Russian Customs Academy, 16v, Strelkovaya str., Vladivostok, 690034, Russia

Abstract: 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.

UDC: 517.51

MSC: 46E35, 31C45

Received August 23, 2021, published March 11, 2022

Language: English

DOI: 10.33048/semi.2022.19.014

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© Steklov Math. Inst. of RAS, 2025