Kato-Ponce inequalities on weighted and variable Lebesgue spaces (1601.06854v2)

Published 26 Jan 2016 in math.AP

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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