English

Compact bilinear operators and paraproducts revisited

Functional Analysis 2024-06-11 v2 Classical Analysis and ODEs

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.

Keywords

Cite

@article{arxiv.2405.08412,
  title  = {Compact bilinear operators and paraproducts revisited},
  author = {Árpád Bényi and Guopeng Li and Tadahiro Oh and Rodolfo H. Torres},
  journal= {arXiv preprint arXiv:2405.08412},
  year   = {2024}
}

Comments

15 pages. Minor updates. To appear in Canad. Math. Bull

R2 v1 2026-06-28T16:26:35.193Z