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For a meromorphic function f in the unit disc, let the ρ∞-order of the growth be the limit of the orders of Lp-norms of log |f(reiθ)| 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.

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