Hostname: page-component-8448b6f56d-c47g7 Total loading time: 0 Render date: 2024-04-16T13:47:26.966Z Has data issue: false hasContentIssue false

The Dual of Hp(R+n+1) for p < 1

Published online by Cambridge University Press:  20 November 2018

T. Walsh*
Affiliation:
University of Florida, Gainesville, Florida
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The dual of Hp of the unit disk for 0 < p < 1 has been characterized by Duren, Romberg and Shields (see [3]). The present paper is concerned with the analogous result for Hp(R+n+1) in the sense of Stein and Weiss (see [11]). In this connection it may be recalled that the dual of H1 has been characterized by Fefferman (see [4]).

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Calderón, A. P., Intermediate spaces and interpolation, the complex method, Studia Math. 24 (1964), 113190.Google Scholar
2. Calderón, A. P. and Zygmund, A., On higher gradients of harmonic functions, Studia Math. 24 (1964), 211226.Google Scholar
3. Duren, P. L., Romberg, B. W., and Shields, A. L., Linear functionals on Hp spaces with 0 < p < 1, J. Reine Angew. Math. 288 (1969), 3260.Google Scholar
4. Fefferman, C., Characterizations of bounded mean oscillation, Bull. Amer. Math. Soc. 77 (1971), 587588.Google Scholar
5. Flett, T. M., On the rate of growth of mean values of holomorphic and harmonic functions, Proc. London Math. Soc. 20 (1970), 749768.Google Scholar
6. Herz, C. S., Lipschitz spaces and Bernstein's theorem on absolutely convergent Fourier transforms, J. Math. Mech. 18 (1968), 283323.Google Scholar
7. Hörmander, L., An introduction to complex analysis in several variables (van Nostrand, Princeton, 1966).Google Scholar
8. Kelley, J. L. and Namioka, I., Linear topological spaces (van Nostrand, Princeton, 1963).Google Scholar
9. de Leeuw, K., Bandch spaces of Lipschitz functions, Studia Math. 21 (1961) 5566.Google Scholar
10. Stein, E. M., On the theory of harmonic functions of several variables, II. Behaviour near the boundary, Acta Math. 106 (1961), 137174.Google Scholar
11. Stein, E. M. and Weiss, G., On the theory of harmonic functions of several variables, I. The theory of H? spaces, Acta Math. 103 (1960), 25-62.Google Scholar
12. Taibleson, M. H., On the theory of Lipschitz spaces of distributions on Euclidean n-space, J. Math. Mech. 13 (1964), 407-479.Google Scholar
13. Weiss, G., Analisis armonico en varias variables. Teoria de los espacios H?, Cursos y Seminarios de Matematica, fasc. 9, Universidad de Buenos Aires, 1960.Google Scholar
14. Zygmund, A., Trigonometric series, Vol. I, 2nd ed. (Cambridge University Press, New York, 1959).Google Scholar