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arXiv · 2102.13535

Off-diagonal estimates for bilinear commutators

Tuomas Oikari
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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 $L^p\times L^q\to L^r,$ $1 \frac{1}{2},$ 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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Tuomas Oikari. 2021-02-26. Off-diagonal estimates for bilinear commutators. https://doi.org/10.1007/s11118-022-09998-5

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