Analysis Seminar: Weighted Multifactor Kato-Ponce Inequalities

Speaker: Sean Douglas, University of Missouri

Abstract: We prove the Kato-Ponce inequality for multiple factors, that is we obtain a Leibniz rule involving Lebesgue norms for the product of $m$ functions $ f_1 \cdots f_m$. We also obtain multifactor Kato-Ponce inequalities in the Muckenhoupt and polynomial weighted setting. Our work contains the endpoint cases in both of these weighted settings building on and extending known bilinear results. In particular we attain the $L^1$ endpoint case for Muckenhoupt weights.

 

Host: Brett Wick