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

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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.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade de Aveiro, 3810-193, Aveiro, Portugal

    Alexandre Almeida

  2. Faculdade de Ciências e Tecnologia, Universidade do Algarve, Campus de Gambelas, 8005-139, Faro, Portugal

    Stefan Samko

Authors
  1. Alexandre Almeida
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  2. Stefan Samko
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Correspondence to Alexandre Almeida.

Additional information

This research was supported in part by INTAS Grant Ref. No. 06-1000017-8792 through the project Variable Exponent Analysis. The first author was also supported by Unidade de Investigação “Matemática e Aplicações” (UIMA) of University of Aveiro and the second author was also partially supported by “Centro de Análise Funcional” (CEAF) of Superior Technical Institute, Lisbon.

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Almeida, A., Samko, S. Fractional and Hypersingular Operators in Variable Exponent Spaces on Metric Measure Spaces. Mediterr. J. Math. 6, 215–232 (2009). https://doi.org/10.1007/s00009-009-0006-7

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  • DOI: https://doi.org/10.1007/s00009-009-0006-7

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