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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.33 no.1 Antofagasta Mar. 2014

http://dx.doi.org/10.4067/S0716-09172014000100004 

 

Hardy-Type Spaces and its Dual

 

René Erlín Castillo
Universidad Nacional de Colombia, Colombia

Julio C. Ramos Fernández and Eduard Trousselot
Universidad de Oriente, Venezuela


ABSATRACT

In this paper we defined a new Hardy-type spaces using atoms on homogeneous spaces which we call H φ,q. Also we prove that under certain conditions BMO φ(p) is the dual of H φ,q.

Keywords : BMO, Dual space, Hardy space, Space of homogeneous type.

Subjclass [2010] : 32A37; 43A85.


 

REFERENCES

[1] Castillo, R. E., Ramos Fernandez, J. C. and Trousselot, E. Functions of Bounded (ö,ñ) Mean Oscillation. Proyecciones Journal of Math. Vol 27, No. 2, pp. 163-177, August (2008).

[2] Coifman, R. R, A real variable characterization of Hp. Studia Math. 51, pp. 269-274, (1974).

[3] Coifman, R. R and Weiss, G. Extensions of Hardy spaces and their use in Analysis. Bull. Amer. Math. Soc. 83, pp. 99-157, (1977).

[4] Duren, P. L., Romberg, B. W. and Shields, A. L., Linear functionals on Hp spaces with 0 <p< 1. J. Reine Angew, Math 238, pp. 32-60, (1969).

[5] Janson, S. Generalization of Lipschitz spaces and an application to Hardy space and bounded mean oscillation. Duke Math. 47, pp. 959982, (1980).

[6] Latter, R. A. A characterization of Hp(Rn) in terms of atoms. Shidia Math 62 (1978) pp. 93-101, (1978).

[7] Macias, R. and Segovia, C. Lipschitz functions on space of homogeneous type, Avd. Math., 33, pp. 257-270, (1979).

 

René Erlín Castillo
Departamento de Matemáticas, Universidad Nacional de Colombia
AP360354 Bogotá e-mail : recastillo@unal.edu.co

Julio C. Ramos Fernández
Departamento de Matemáticas, Universidad de Oriente 6101 Cumanáa, Edo. Sucre, Venezuela
e-mail : jcramos@udo.edu.ve

Eduard Trousselot
Departamento de Matemaáticas, Universidad de Oriente 6101 Cumaná, Edo. Sucre, Venezuela
e-mail : eddycharles2007@hotmail.com

Received : August 2012. Accepted : October 2013.

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