LAUSR

We provide the weak factorization of the Hardy spaces Hp(ℝ+, dmλ) in the Bessel setting, for $$p \in (\frac{2\lambda+1}{2\lambda+2}, 1]$$p∈(2λ+12λ+2,1]. As a corollary we obtain a characterization of the boundedness of the commutator [b,$${R_{{\Delta _\lambda }}}$$RΔλ] from Lq(ℝ+, dmλ) to Lr(ℝ+, dmλ) when b ∈ Lipα(ℝ+, dmλ) provided that $$\alpha = \frac{1}{q} - \frac{1}{r}$$α=1q−1r. The results are an adaptation and modification of the work of Duong, Li, Yang, and the second named author, which only considered the case of p = 1, which in turn are based on modifications and adaptations of work by Uchiyama.