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.
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