Some propeties of the space D_{2}(mu)

For a finite positive Borel measure $mu$ on the unit circle the space $D_{2}(mu)$, consists of functions in the Dirichlet type space $D(mu)$ whose derivatives are in the Hardy space. We prove that polynomials are dense in $D_{2}(mu)$ and give several equivalent conditions under which the monomials $z^n$ are orthogonal in this space.