Weighted Bergman spaces and Carleson measures on the unit ball of \(\mathbb C^n\) (Q5932665)

Let \(\phi\) be a normal function on \([0,1)\), \(B_n\) the unit ball of \(\mathbb C^n\), and \(A^p_\phi(B_n)\) the weighted Bergman spaces on \(B_n\) with weight \(\phi\). The author presents three results characterizing bounded resp. compact Carleson measures \(\mu\) on \(B_n\) in terms of connections between the norms of \(A^p_\phi\) and \(L^p_\mu\).