Weak Factorization of Hardy Spaces in the Bessel Setting

R. Oliver; B. D. Wick

doi:10.1007/s10476-018-0610-5

Weak Factorization of Hardy Spaces in the Bessel Setting

R. Oliver, B. D. Wick

Department of Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We provide the weak factorization of the Hardy spaces H^p(ℝ₊, dm_λ) in the Bessel setting, for p∈(2λ+12λ+2,1]. As a corollary we obtain a characterization of the boundedness of the commutator [b,RΔλ] from L^q(ℝ₊, dm_λ) to L_r(ℝ₊, dm_λ) when b ∈ Lip_α(ℝ₊, dm_λ) provided that 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.

Original language	English
Pages (from-to)	391-411
Number of pages	21
Journal	Analysis Mathematica
Volume	45
Issue number	2
DOIs	https://doi.org/10.1007/s10476-018-0610-5
State	Published - Jun 1 2019

Keywords

BMO
Calderón-Zygmund operator
commutator
Hardy space
weak factorization

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10.1007/s10476-018-0610-5

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AU - Wick, B. D.

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N2 - We provide the weak factorization of the Hardy spaces Hp(ℝ+, dmλ) in the Bessel setting, for p∈(2λ+12λ+2,1]. As a corollary we obtain a characterization of the boundedness of the commutator [b,RΔλ] from Lq(ℝ+, dmλ) to Lr(ℝ+, dmλ) when b ∈ Lipα(ℝ+, dmλ) provided that 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.

AB - We provide the weak factorization of the Hardy spaces Hp(ℝ+, dmλ) in the Bessel setting, for p∈(2λ+12λ+2,1]. As a corollary we obtain a characterization of the boundedness of the commutator [b,RΔλ] from Lq(ℝ+, dmλ) to Lr(ℝ+, dmλ) when b ∈ Lipα(ℝ+, dmλ) provided that 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.

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KW - Calderón-Zygmund operator

KW - commutator

KW - Hardy space

KW - weak factorization

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SP - 391

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JO - Analysis Mathematica

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Weak Factorization of Hardy Spaces in the Bessel Setting

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