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Lemma 3 in Chapter 16 of Coifman-Meyer's Wavelets: Calderón-Zygmund and Multilinear Operators is used to prove just this for the inhomogeneous paraproduct. It might be worth looking at to see if you could extend that argument to work in your case. Granted, this comment may no longer be relevant a year later...
Do any of Arkeryd's papers explicitly employ nonstandard methods outside of the couple expository/survey-type articles on NSA? Or does he generally employ nonstandard methods "behind the scenes"?
This is an old post, so you may no longer be interested in the paper. However, if you are, I have a copy. I don't have a link or anything, but I'd be happy to email it to you.
