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arXiv · 2406.13174

Multilinear paraproducts on Sobolev spaces

Francesco Di Plinio·A. Walton Green·Brett D. Wick
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Abstract

Paraproducts are a special subclass of the multilinear Calder\'on-Zygmund operators, and their Lebesgue space estimates in the full multilinear range are characterized by the $\mathrm{BMO}$ norm of the symbol. In this note, we characterize the Sobolev space boundedness properties of multilinear paraproducts in terms of a suitable family of Triebel-Lizorkin type norms of the symbol. Coupled with a suitable wavelet representation theorem, this characterization leads to a new family of Sobolev space $T(1)$-type theorems for multilinear Calder\'on-Zygmund operators.

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Francesco Di Plinio, A. Walton Green, Brett D. Wick. 2024-06-19. Multilinear paraproducts on Sobolev spaces. https://arxiv.org/abs/2406.13174

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