Abstract
We obtain sharp necessary conditions on the counting function of zeros of analytic functions from Bergman spaces with standard weight and from spaces which are their natural generalization.
Similar content being viewed by others
References
S. V. Shvedenko, “Hardy classes and related spaces of analytic functions in the unit disc, polydisc and ball,” in Itogi Nauki i Tekhniki Ser.Mat. Analiz (VINITI, Moscow, 1985), Vol. 23, pp. 3–124 [in Russian].
H. S. Shapiro and A. L. Shields, “On zeros of the functions with finite Dirichlet integral and some related function spaces,” Math. Z. 80, 217–229 (1962).
C. Horowitz, “Zeros of the functions in the Bergman spaces,” Duke Math. J. 41(4), 693–710 (1974).
E. Beller, “Zeros of A p functions and related classes of analytic functions,” Israel J. Math. 22(1), 68–80 (1975).
A. M. Sedletskii, “Zeros of analytic functions of the classes A pα ,” in Current Problems in Function Theory (Teberda, 1985) (Rostov. Gos. Univ., Rostov-on-Don, 1987), pp. 24–29 [in Russian].
A. M. Sedletskii, “Analytic Fourier transforms and exponential approximations. II,” in Sovrem.Mat. Fundam. Napravl. (MAI, Moscow, 2003), Vol. 6, pp. 3–162 [J. Math. Sci. (N. Y.) 130 (6), 5083–5254 (2005)].
E. A. Sevast’yanov and A. A. Dolgoborodov, “On the distribution of zeros of functions from weighted Bergman spaces,” Mat. Zametki 86(1), 95–109 (2009) [Math. Notes 86 (1–2), 93–106 (2009)].
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A. A. Dolgoborodov, 2010, published in Matematicheskie Zametki, 2010, Vol. 88, No. 2, pp. 201–216.
Rights and permissions
About this article
Cite this article
Dolgoborodov, A.A. On the zeros of functions from Bergman spaces and some related spaces. Math Notes 88, 183–197 (2010). https://doi.org/10.1134/S0001434610070187
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0001434610070187