Norm estimates for the fractional derivative of multiple factors

We extend the Kato-Ponce inequality to a product of m functions, proving an estimate currently missing from the literature. This study is motivated by the fact that the 3-factor Kato-Ponce does not follow directly from the 2-factor version in the full range of permissible indices. Our methodology is...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 537; no. 2; p. 128409
Main Authors Douglas, Sean, Grafakos, Loukas
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.09.2024
Subjects
Fractional derivatives
Kato-Ponce
Littlewood-Paley theory
Multi-factored
Normed fractional Leibniz rules
Paraproducts
Littlewood-Paley theory
Paraproducts
Fractional derivatives
Kato-Ponce
Normed fractional Leibniz rules
Multi-factored
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Summary:We extend the Kato-Ponce inequality to a product of m functions, proving an estimate currently missing from the literature. This study is motivated by the fact that the 3-factor Kato-Ponce does not follow directly from the 2-factor version in the full range of permissible indices. Our methodology is based upon that in [12] but our extension entails a novel decomposition that elegantly and effectively handles the technical difficulties that arise from the combinatorial complexity of the possibly large number of factors.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2024.128409