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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.32 no.4 Antofagasta dic. 2013

http://dx.doi.org/10.4067/S0716-09172013000400001 

 

A convergence result for unconditional series in Lp(μ)

 

Juan M. Medina, Bruno Cernuschi-Frías
Universidad de Buenos Aires, Argentina


ABSTRACT

We give sufficient conditions for the convergence almost everywhere of the expansion with respect to an unconditional basis for functions in Lp p > 2. This result extends the classical theorem of Menchoff and Rademacher for orthogonal series in L2.

Subjclass 2000 MSC Primary 42C15 ; Secondary: 46B15, 46B20.

Keywords : Unconditional basic sequence, almost sure convergence, random series.


 

REFERENCES

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Juan M. Medina
Departamento de Matematica,
Instituto Argentino de Matematica,
Universidad de Buenos Aires,
Paseo Colion 850 (1063)
Capital Federal
CONICET
Argentina
e-mail : jmedina@fi.uba.ar

 

Bruno Cernuschi—Frías
Facultad de Ingeniería
Instituto Argentino de Matematica
Universidad de Buenos Aires
Paseo Colion 850 (1063)
Capital Federal
CONICET
Argentina
e-mail : bcf@ieee.org

*This work was partially supported by the Universidad de Buenos Aires, grant No. UBACyT 20020100100503, and the Consejo Nacional de Investigaciones Científicas y Tecnicas, CONICET, Argentina.

Received : May 2012. Accepted : July 2013.

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