Analytical findings reveal the conditions for boundedness in Lorentz spaces for Riesz transform commutators.
Let [Formula: see text] and [Formula: see text] be the Riesz transform associated with [Formula: see text], where [Formula: see text] is the Bessel operator on [Formula: see text]. In this paper, the authors show that the Riesz commutator [Formula: see text] is bounded (compact respectively) on the Lorentz space [Formula: see text] if and only if [Formula: see text]([Formula: see text] respectively), where [Formula: see text] and [Formula: see text].
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Hu et al. (2026) studied this question.
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