Weak factorization of Hardy spaces in the Bessel setting

2016/04/08 by Oliver, Roc, Wick, Brett D.
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1604.02409

Abstract

We provide the weak factorization of the Hardy spaces H^p(ℝ₊, dm_λ) in the Bessel setting, for p∈ ((2λ+ 1)/(2λ+ 2), 1]. As a corollary we obtain a characterization of the boundedness of the commutator [b, R_Δλ] from L^q(ℝ₊, dm_λ) to L^r(ℝ₊, dm_λ) when b∈ \textrmLip_α(ℝ₊, dm_λ) provided that α= (1)/(q) - (1)/(r). The results are a slight generalization and modification of the work of Duong, Li, Yang, and the second named author, which in turn are based on modifications and adaptations of work by Uchiyama.

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