Dirichlet spaces of domains bounded by quasicircles

Research output: Contribution to journalArticleScientificpeer-review


Research units

  • 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.


Original languageEnglish
JournalCommunications in Contemporary Mathematics
Publication statusE-pub ahead of print - 1 Jan 2019
MoE publication typeA1 Journal article-refereed

    Research areas

  • Dirichlet spaces, Faber operator, Faber series, Grunsky operator, multiply-connected domains, quasicircles

ID: 40178236