English

Kato-Ponce inequalities on weighted and variable Lebesgue spaces

Analysis of PDEs 2016-05-24 v2

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.

Keywords

Cite

@article{arxiv.1601.06854,
  title  = {Kato-Ponce inequalities on weighted and variable Lebesgue spaces},
  author = {David Cruz-Uribe and Virginia Naibo},
  journal= {arXiv preprint arXiv:1601.06854},
  year   = {2016}
}

Comments

Revised version contains corrections from referees report and new section Kato-Ponce inequalities in Lorentz and Morrey spaces