Multilinear paraproducts on Sobolev spaces
Classical Analysis and ODEs
2024-06-21 v1 Analysis of PDEs
Functional Analysis
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 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 -type theorems for multilinear Calder\'on-Zygmund operators.
Cite
@article{arxiv.2406.13174,
title = {Multilinear paraproducts on Sobolev spaces},
author = {Francesco Di Plinio and A. Walton Green and Brett D. Wick},
journal= {arXiv preprint arXiv:2406.13174},
year = {2024}
}