Interpolating sequences and embedding theorems in weighted Bergman spaces
For \(0<p<\infty\), let \(L^p_a(\mu)\) denote the weighted Bergman space on the unit disk \(D\) in the complex plane, where \(\mu\) is a finite positive Borel measure on \(D\). When \(\mu\) is an absolutely continuous measure which satisfies an \((A_p)\)-condition, we study interpolating sequences on \(L^p_a (\mu)\) and give several sufficient conditions in order that such a sequence exists in \(L^p_a (\mu)\). Using them, we obtain embedding theorems for weighted Bergman spaces between \(L^p_a (\mu)\) and \(L^q_a (\nu)\), where \(\nu\) is a finite positive Borel measure on \(D\) and \(0<q <\infty\).
scientific article; zbMATH DE number 1011282