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.
David Cruz-Uribe. Virginia Naibo. "Kato-Ponce inequalities on weighted and variable Lebesgue spaces." Differential Integral Equations 29 (9/10) 801 - 836, September/October 2016. https://doi.org/10.57262/die/1465912605