Summary: FUNCTION SPACES RELATED TO THE DIRICHLET SPACE
N. ARCOZZI
We report on recent joint work with R. Rochberg, E. Sawyer and B. Wick, related with the
holomorphic Dirichlet space and we contextualize it within the general theory.
1. An old and prestigious story: the Hardy space.
Consider the Hardy space H2 in the unit disc D,
f(z) =
X
n=0
anzn
= f 2
H2 =
X
n=0
|an|2
.
The multiplier space of H2, containing all g's holomorphic in D such that the operator f gf
is bounded on H2, is M(H2) = H, the space of the bounded holomorphic functions. We also
have that
H2

Source: Arcozzi, Nicola - Dipartimento di Matematica, Università di Bologna

Collections: Mathematics