Multi-parameter flag Leibniz rules of arbitrary complexity in mixed-norm spaces

Abstract

We prove multi-parameter Leibniz rules corresponding to flag paraproducts of arbitrary complexity in mixed-norm spaces, including endpoint estimates. The proof relies on multi-linear harmonic analysis techniques and a quantitative treatment of the commutators introduced by Bourgain and Li. The argument is robust and applicable to a generic class of multipliers, including (symmetric) Mikhlin multipliers of positive order and asymmetric variants of partial differential operators and Mikhlin multipliers of positive order.

arXiv comment78 pages, 15 figures

References in corpus (3)

• Multiple Vector Valued Inequalities via the Helicoidal Method
• A remark on an endpoint Kato-Ponce inequality
• Five-Linear Singular Integral Estimates of Brascamp-Lieb Type