An integral formula in weighted Bergman spaces (Q977098)

This paper is best described by its abstract: ``In order to establish that extremal functions in the Bergman space \(A^p\) act as both expansive multipliers and contractive divisors, \textit{P. Duren, D. Khavinson, H. S. Shapiro} and \textit{C. Sundberg} [Pac. J. Math. 157, No.1, 37--56 (1993; Zbl 0739.30029)] made use of an integral formula involving the biharmonic Green function. Using a weighted biharmonic Green function, we derive an analogous integral formula in the standard weighted Bergman space \(A^p_\alpha\) when \(\alpha=1\), and we also discuss how the formula can be established for general \(\alpha\). Moreover, we show that each \(A^p_1\)-inner function acts as a contractive divisor on the invariant subspace which it generates.''