Zeros of functions in weighted spaces with mixed norm

Abstract

In the spaces of analytic functions f in the unit disk with mixed norm and measure satisfying the Δ2-condition, sharp necessary conditions on subsequences of zeros \(\{ z_{n_k } (f)\} \) of the function f are obtained in terms of subsequences of numbers {nk}. These conditions can be used to define, in the spaces with mixed norm, subsets of functions with certain extremal properties; these subsets provide answers to a number of questions about the zero sets of the spaces under consideration and, in particular, about weighted Bergman spaces.