Potential Analysis

, Volume 46, Issue 3, pp 499–525 | Cite as

Characterization of Lipschitz Functions via the Commutators of Singular and Fractional Integral Operators in Variable Lebesgue Spaces

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Abstract

We obtain characterizations of a variable version of Lipschitz spaces in terms of the boundedness of commutators of Calderón-Zygmund and fractional type operators in the context of the variable exponent Lebesgue spaces L p(⋅), where the symbols of the commutators belong to the Lipschitz spaces. A useful tool is a pointwise estimate involving the sharp maximal operator of the commutator and certain associated maximal operators, which is new even in the classical context. Some boundedness properties of the commutators between Lebesgue and Lipschitz spaces in the variable context are also proved.

Keywords

Variable exponent spaces Lipschitz spaces Maximal sharp operator Fractional integrals Commutators operators 

Mathematics Subject Classification (2010)

42B25 42B35 

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Departamento de MatemáticaFacultad de Ingeniería Química (UNL)Santa FeArgentina
  2. 2.Departamento de Matemática (FaCENA-UNNE)CONICETCorrientesArgentina

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