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Revista Matemática Complutense

, Volume 30, Issue 2, pp 369–392 | Cite as

Lebesgue inequalities for the greedy algorithm in general bases

  • Pablo M. Berná
  • Óscar Blasco
  • Gustavo GarrigósEmail author
Article

Abstract

We present various estimates for the Lebesgue type inequalities associated with the thresholding greedy algorithm, in the case of general bases in Banach spaces. We show the optimality of the involved constants in some situations. Our results recover and slightly improve various estimates appearing earlier in the literature.

Keywords

Thresholding greedy algorithm Quasi-greedy basis Conditional basis 

Mathematics Subject Classification

41A65 41A46 46B15 

Notes

Acknowledgements

we wish to thank F. Albiac, J.L. Ansorena and E. Hernández for many useful conversations about these topics. We also thank the anonymous referee for the careful reading and useful comments.

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Copyright information

© Universidad Complutense de Madrid 2017

Authors and Affiliations

  • Pablo M. Berná
    • 1
  • Óscar Blasco
    • 2
  • Gustavo Garrigós
    • 3
    Email author
  1. 1.Instituto Universitario de Matemática Pura y AplicadaUniversitat Politècnica de ValènciaValenciaSpain
  2. 2.Departamento de Análisis MatemáticoUniversidad de ValenciaValenciaSpain
  3. 3.Departamento de MatemáticasUniversidad de MurciaMurciaSpain

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