Hardy-Type Spaces and its Dual
DOI:
https://doi.org/10.4067/S0716-09172014000100004Keywords:
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.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).
[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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