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Potential Analysis

, Volume 51, Issue 4, pp 579–601 | Cite as

Commutators of Singular Integrals with Kernels Satisfying Generalized Hörmander Conditions and Extrapolation Results to the Variable Exponent Spaces

  • Luciana MelchioriEmail author
  • Gladis Pradolini
Article
  • 47 Downloads

Abstract

We obtain boundedness results for the higher order commutators of singular integral operators between weighted Lebesgue spaces, including Lp-BMO and Lp-Lipschitz estimates. The kernels of such operators satisfy certain regularity condition, and the symbol of the commutator belongs to a Lipschitz class. We also deal with commutators of singular integral operators with less regular kernels satisfying a Hörmander’s type inequality. Moreover, we give a characterization result involving symbols of the commutators and continuity results for extreme values of p. Finally, by extrapolation techniques, we derive different results in the variable exponent context.

Keywords

Commutators Variable Lebesgue spaces Extrapolation 

Mathematics Subject Classification (2010)

42B25 

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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Facultad de Ingeniería QuímicaCONICET-UNLSanta FeArgentina

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