Bellman functions and $L^p$ estimates for paraproducts
Probability
2019-02-04 v3 Classical Analysis and ODEs
Abstract
We give an explicit formula for one possible Bellman function associated with the boundedness of dyadic paraproducts regarded as bilinear operators or trilinear forms. Then we apply the same Bellman function in various other settings, to give self-contained alternative proofs of the estimates for several classical operators. These include the martingale paraproducts of Ba\~{n}uelos and Bennett and the paraproducts with respect to the heat flows.
Keywords
Cite
@article{arxiv.1609.02895,
title = {Bellman functions and $L^p$ estimates for paraproducts},
author = {Vjekoslav Kovač and Kristina Ana Škreb},
journal= {arXiv preprint arXiv:1609.02895},
year = {2019}
}
Comments
18 pages, 1 figure, 1 ancillary file (Mathematica notebook); v3: exposition is slightly improved, additional calculations and remarks included