Compact bilinear operators and paraproducts revisited
\'Arp\'ad B\'enyi, Guopeng Li, Tadahiro Oh, and Rodolfo H. Torres
TL;DR
This paper provides a new proof of the compactness of bilinear paraproducts with CMO symbols, extending the understanding of compact bilinear operators through properties, examples, and advanced analytical techniques.
Contribution
It introduces a novel proof approach for compactness of bilinear paraproducts with CMO symbols, linking properties of bilinear operators with Carleson measures and interpolation methods.
Findings
Established new properties of compact bilinear operators.
Proved compactness of bilinear paraproducts with CMO symbols.
Connected bilinear compactness with Carleson measure estimates.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsNumerical methods in inverse problems · Holomorphic and Operator Theory · Spectral Theory in Mathematical Physics