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arXiv · 2405.08412

Compact bilinear operators and paraproducts revisited

Árpád Bényi·Guopeng Li·Tadahiro Oh·Rodolfo H. Torres
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Abstract

We present a new proof of the compactness of bilinear paraproducts with CMO symbols. By drawing an analogy to compact linear operators, we first explore further properties of compact bilinear operators on Banach spaces and present examples. We then prove compactness of bilinear paraproducts with CMO symbols by combining one of the properties of compact bilinear operators thus obtained with vanishing Carleson measure estimates and interpolation of bilinear compactness.

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Árpád Bényi, Guopeng Li, Tadahiro Oh, Rodolfo H. Torres. 2024-06-09. Compact bilinear operators and paraproducts revisited. https://arxiv.org/abs/2405.08412

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