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We consider the embedding of integrable Teichm\"uller spaces Tₚ into analytic Besov spaces by using pre-Schwarzian derivatives. Unlike the case of the Bers embedding by Schwarzian derivatives, there is a big difference between the cases p>1 and p=1. In this paper, we focus on the case p=1 and generalize the previous results obtained for p>1. This gives a unified approach to the complex analytic theory of integrable Teichm\"uller spaces Tₚ for all p 1.
Wei et al. (Wed,) studied this question.