Zero distribution and factorization of analytic functions of slow growth in the unit disc

Chyzhykov, I.

doi:10.1090/S0002-9939-2012-11463-7

Zero distribution and factorization of analytic functions of slow growth in the unit disc
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Proc. Amer. Math. Soc. 141 (2013), 1297-1311 Request permission

Abstract:

For a meromorphic function $f$ in the unit disc, let the $\rho _\infty$-order of the growth be the limit of the orders of $L_p$-norms of $\log |f(re^{i\theta })|$ over the circle. In the case when the order of the maximum modulus function is smaller than 1, we describe zero distribution of canonical products and derive a new factorization theorem and logarithmic derivative estimates.

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