The Kato-Ponce Inequality

2013/03/21 by Loukas Grafakos, Grafakos, Loukas, Seungly Oh +1 · 7 citations
Mathematics · #Advanced Mathematical Physics Problems #Nonlinear Partial Differential Equations #Advanced Harmonic Analysis Research

paper · pdf · doi:10.48550/arxiv.1303.5144

Abstract

In this article we develop a simplistic approach to revisit the classical Kato-Ponce inequality, which is also known as 'fractional Leibniz rule.' As a consequence, we derive the validity of this inequality even in quasi-Banach spaces L^p for p<1 with a certain restrictions on the indices. Also, we display the sharpness of this restriction by means of a counter-example. Finally, we also prove a multi-parameter variant of the inequality, which allows for partial fractional derivatives on Rⁿ.

Citations

• Interpolation of linear operators
• Some Maximal Inequalities

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