Abstract
We find a minimal notion of non-degeneracy for bilinear singular integral operators T and identify testing conditions on the multiplying function b that characterize the Lp × Lq → Lr, \(1<p,q<\infty \) and \(r>\frac {1}{2},\) boundedness of the bilinear commutator [b, T]1(f, g) = bT(f, g) − T(bf, g). Our arguments cover almost all arrangements of the integrability exponents p, q, r with a single open problem presented in the end. Additionally, the arguments extend to the multilinear setting.
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I thank Henri Martikainen for helpful discussions and comments.
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T. Oikari was supported by the Academy of Finland project No. 306901, by the Finnish Centre of Excellence in Analysis and Dynamics Research project No. 307333, and by the three-year research grant of the University of Helsinki No. 75160010.
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Oikari, T. Off-Diagonal Estimates for Bilinear Commutators. Potential Anal 59, 1079–1105 (2023). https://doi.org/10.1007/s11118-022-09998-5
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DOI: https://doi.org/10.1007/s11118-022-09998-5