Mediterranean Journal of Mathematics

, Volume 6, Issue 2, pp 215–232 | Cite as

Fractional and Hypersingular Operators in Variable Exponent Spaces on Metric Measure Spaces

Article

Abstract

We prove the continuity of potential type operators and hypersingular operators in variable Lebesgue and Sobolev spaces on a metric measure space (Χ, d, µ). Two variants of such operators are considered, according to the regularity admitted on the measure µ.

Mathematics Subject Classification (2000)

Primary 43A85 26A33 Secondary 42B25 46E35 26D10 

Keywords

Fractional integrals hypersingular integrals maximal functions variable exponents metric measure space Ahlfors regularity 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  1. 1.Departamento de MatemáticaUniversidade de AveiroAveiroPortugal
  2. 2.Faculdade de Ciências e TecnologiaUniversidade do AlgarveFaroPortugal

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