Differential and Integral Equations

Kato-Ponce inequalities on weighted and variable Lebesgue spaces

David Cruz-Uribe and 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.

Article information

Source
Differential Integral Equations Volume 29, Number 9/10 (2016), 801-836.

Dates
First available in Project Euclid: 14 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.die/1465912605

Mathematical Reviews number (MathSciNet)
MR3513582

Zentralblatt MATH identifier
06644050

Subjects
Primary: 42B25: Maximal functions, Littlewood-Paley theory 42B35: Function spaces arising in harmonic analysis 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems 47G40: Potential operators [See also 31-XX]

Citation

Cruz-Uribe, David; Naibo, Virginia. Kato-Ponce inequalities on weighted and variable Lebesgue spaces. Differential Integral Equations 29 (2016), no. 9/10, 801--836. https://projecteuclid.org/euclid.die/1465912605.


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