The Kato-Ponce Inequality

Loukas Grafakos; Seungly Oh

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arXiv · 1303.5144

The Kato-Ponce Inequality

Loukas Grafakos·Seungly Oh

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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 $R^n$.

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Loukas Grafakos, Seungly Oh. 2013-03-21. The Kato-Ponce Inequality. https://arxiv.org/abs/1303.5144

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