First we introduce the Bailleul-Hoshinos result [4], which links the theory of regularity structures and the paracontrolled calculus. As an application of their result, we give another algebraic proof of the multicomponent commutator estimate [3], which is a generalized version of the Gubinelli-Imkeller-Perkowskis commutator estimate [11, Lemma 2.4].
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