Möbius-invariant Hilbert spaces in polydiscs
Möbius-invariant Hilbert spaces in polydiscs
We define the Dirichlet space 31 on the unit polydisc U" of C" . 2 is a semi-Hilbert space of of holomorphic functions, contains the holomorphic polynomials densely, is invariant under compositions with the biholomorphic automorphisms of U" , and its semi-norm is preserved under such compositions.We show that 2 …