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arXiv · 1601.06854

Kato-Ponce inequalities on weighted and variable Lebesgue spaces

David Cruz-Uribe·Virginia Naibo
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Abstract

We prove fractional Leibniz rules and related commutator estimates in the settings of weighted and variable Lebesgue spaces. Our main tools are uniform weighted estimates for sequences of square-function-type operators and a bilinear extrapolation theorem. We also give applications of the extrapolation theorem to the boundedness on variable Lebesgue spaces of certain bilinear multiplier operators and singular integrals.

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David Cruz-Uribe, Virginia Naibo. 2016-05-23. Kato-Ponce inequalities on weighted and variable Lebesgue spaces. https://arxiv.org/abs/1601.06854

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