Weak factorization of the Hardy space H^p for small values of p, in the multilinear setting

2018/02/06 by Kuffner, Marie-Jose S.
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1802.01768

Abstract

We give a weak factorization proof of the Hardy space H^p(ℝⁿ) in the multilinear setting, for (n)/(n+1) < p <1. As a consequence, we obtain a characterization of the boundedness of the commutator [b,T] from L^r₁(\mathbb Rⁿ) ~x ... x~ L^r_m (\mathbb Rⁿ) to L^{q^′} (\mathbb Rⁿ), where b ∈ Lip_α(\mathbb Rⁿ), and \fracαn = ∑_i=1^m \frac1r_i +(1)/(q) - 1.

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