Weak Factorization of Hardy Spaces in the Bessel Setting

We provide the weak factorization of the Hardy spaces H p (ℝ + , dm λ ) in the Bessel setting, for p ∈ ( 2 λ + 1 2 λ + 2 , 1 ] . As a corollary we obtain a characterization of the boundedness of the commutator [ b , R Δ λ ] from L q (ℝ + , dm λ ) to L r (ℝ + , dm λ ) when b ∈ Lip α (ℝ + , dm λ ) pro...

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Bibliographic Details
Published in:Analysis mathematica (Budapest) 2019-06, Vol.45 (2), p.391-411
Main Authors: Oliver, R., Wick, B. D.
Format: Article
Language:English
Subjects:
Analysis
Commutators
Factorization
Mathematics
Mathematics and Statistics
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Summary:We provide the weak factorization of the Hardy spaces H p (ℝ + , dm λ ) in the Bessel setting, for p ∈ ( 2 λ + 1 2 λ + 2 , 1 ] . As a corollary we obtain a characterization of the boundedness of the commutator [ b , R Δ λ ] from L q (ℝ + , dm λ ) to L r (ℝ + , dm λ ) when b ∈ Lip α (ℝ + , dm λ ) provided that α = 1 q − 1 r . 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.
ISSN:0133-3852
1588-273X
DOI:10.1007/s10476-018-0610-5