Hardy-Type Spaces and its Dual

Authors

  • René Erlín Castillo Universidad Nacional de Colombia.
  • Julio César Ramos Fernández Universidad de Oriente.
  • Eduard Trousselot Universidad de Oriente.

DOI:

https://doi.org/10.4067/S0716-09172014000100004

Keywords:

BMO, dual space, Hardy space, space of homogeneous type, oscilación media acotada, espacio de Hardy, espacio homogéneo.

Abstract

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.

Author Biographies

René Erlín Castillo, Universidad Nacional de Colombia.

Departamento de Matemáticas.

Julio César Ramos Fernández, Universidad de Oriente.

Departamento de Matemáticas.

Eduard Trousselot, Universidad de Oriente.

Departamento de Matemáticas.

References

[1] Castillo, R. E., Ramos Fernández, J. C. and Trousselot, E. Functions of Bounded (φ, p) 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. 959-982, (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).

Published

2017-03-23

How to Cite

[1]
R. E. Castillo, J. C. Ramos Fernández, and E. Trousselot, “Hardy-Type Spaces and its Dual”, Proyecciones (Antofagasta, On line), vol. 33, no. 1, pp. 43-59, Mar. 2017.

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