Radnell , D , Schippers , E & Staubach , W 2019 , ' Dirichlet spaces of domains bounded by quasicircles ' , Communications in Contemporary Mathematics , vol. 22 , no. 3 . https://doi.org/10.1142/S0219199719500226
Abstract:
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.
Description:
AVAA TIEDOSTO 12 KK EMBARGOLLA, KUN ARTIKKELI ILMESTYY