Monatshefte für Mathematik

, Volume 188, Issue 4, pp 591–609 | Cite as

Nowhere hölderian functions and Pringsheim singular functions in the disc algebra

  • L. Bernal-González
  • A. Bonilla
  • J. López-Salazar
  • J. B. Seoane-SepúlvedaEmail author


We prove the existence of dense linear subspaces, of infinitely generated subalgebras and of infinite dimensional Banach spaces in the disc algebra all of whose nonzero members are not \(\alpha \)-hölderian at any point of the unit circle for any  \(\alpha >0\). This completes the recently established result of topological genericity of this kind of functions, as well as the corresponding lineability statements about functions that are nowhere differentiable at the boundary. Topological and algebraic genericity is also studied for the family of boundary-smooth holomorphic functions that are Pringsheim singular at any point of the unit circle.


Nowhere hölderian function Pringsheim singular function Disc algebra Lineability Spaceability Algebrability 

Mathematics Subject Classification

Primary 30H50 Secondary 15A03 26A27 26E10 46E10 



The first author was supported by the Plan Andaluz de Investigación de la Junta de Andalucía FQM-127 Grant P08-FQM-03543 and by MEC Grant MTM2015-65242-C2-1-P. The second author was supported by MINECO Project MTM2016-75963-P. The third and fourth authors were supported by MEC Grant MTM2015-65825-P.


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  • L. Bernal-González
    • 1
  • A. Bonilla
    • 2
  • J. López-Salazar
    • 3
  • J. B. Seoane-Sepúlveda
    • 4
    Email author
  1. 1.Departamento de Análisis Matemático Facultad de MatemáticasUniversidad de SevillaSevillaSpain
  2. 2.Departamento de Análisis MatemáticoUniversidad de la LagunaLa LagunaSpain
  3. 3.Departamento de Matemática Aplicada a las Tecnologías de la Información y las Comunicaciones Escuela Técnica Superior de Ingeniería y Sistemas de TelecomunicaciónUniversidad Politécnica de MadridMadridSpain
  4. 4.Instituto de Matemática Interdisciplinar (IMI), Facultad de Ciencias MatemáticasUniversidad Complutense de MadridMadridSpain

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