Weighted reproducing kernels and the Bergman space (Q1933629)

Denote by \([f]_z\) the closed \(z\)-invariant subspace of the Bergman space \(A^2(\mathbb{D})\) generated by a given function \(f\) in \( A^2(\mathbb{D})\), and let \(B\) be a finite or an infinite Blaschke product vanishing at \(0\). The main results of the authors describe the structure of the orthocomplement \([f]_z\cap (B[f]_z)^{\perp}\), of \(B[f]_z\) in \([f]_z\), in terms of the derivatives of a weighted reproducing kernel at the zeros of \(B\).