Dirichlet spaces of domains bounded by quasicircles

Tutkimustuotos: Lehtiartikkeli



  • University of Manitoba
  • Uppsala University


Consider a multiply-connected domain ∑ in the sphere bounded by n non-intersecting quasicircles. We characterize the Dirichlet space of ∑ as an isomorphic image of a direct sum of Dirichlet spaces of the disk under a generalized Faber operator. This Faber operator is constructed using a jump formula for quasicircles and certain spaces of boundary values. Thereafter, we define a Grunsky operator on direct sums of Dirichlet spaces of the disk, and give a second characterization of the Dirichlet space of ∑ as the graph of the generalized Grunsky operator in direct sums of the space 1/2(1) on the circle. This has an interpretation in terms of Fourier decompositions of Dirichlet space functions on the circle.


JulkaisuCommunications in Contemporary Mathematics
TilaSähköinen julkaisu (e-pub) ennen painettua julkistusta - 1 tammikuuta 2019
OKM-julkaisutyyppiA1 Julkaistu artikkeli, soviteltu

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