Geodesic
Zeros of Functions in Weighted Spaces with Mixed Norm
Matematičeskie zametki, Tome 94 (2013) no. 2, pp. 279-294

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In the spaces of analytic functions $f$ in the unit disk with mixed norm and measure satisfying the $\Delta_2$-condition, sharp necessary conditions on subsequences of zeros $\{z_{n_k}(f)\}$ of the function $f$ are obtained in terms of subsequences of numbers $\{n_k\}$. 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.
Keywords: weighted space with mixed norm, weighted Bergman space, distribution of moduli of zeros, zero set of a function, Hardy space. 
@article{MZM_2013_94_2_a10,
     author = {E. A. Sevast'yanov and A. A. Dolgoborodov},
     title = {Zeros of {Functions} in {Weighted} {Spaces} with {Mixed} {Norm}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {279--294},
     publisher = {mathdoc},
     volume = {94},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_94_2_a10/}
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E. A. Sevast'yanov; A. A. Dolgoborodov. Zeros of Functions in Weighted Spaces with Mixed Norm. Matematičeskie zametki, Tome 94 (2013) no. 2, pp. 279-294. http://geodesic.mathdoc.fr/item/MZM_2013_94_2_a10/