Hardy spaces of conjugate temperatures

Martha Guzmán-Partida

ArticleOriginal scientific text

Title

Hardy spaces of conjugate temperatures

Authors ¹

Affiliations

Instituto de Matematicas, Universidad Nacional Autónoma de México, Ciudad Universitaria, México, D.F., 04510, Mexico

Abstract

We define Hardy spaces of pairs of conjugate temperatures on

ℝ_{+}^{2}

using the equations introduced by Kochneff and Sagher. As in the holomorphic case, the Hilbert transform relates both components. We demonstrate that the boundary distributions of our Hardy spaces of conjugate temperatures coincide with the boundary distributions of Hardy spaces of holomorphic functions.

H. S. Bear, Hardy spaces of heat functions, Trans. Amer. Math. Soc. 301 (1987), 831-844.
J. R. Cannon, The One-Dimensional Heat Equation, Encyclopedia Math. Appl. 23, Addison-Wesley, 1984.
C. Fefferman and E. M. Stein, $H^{p}$ spaces of several variables, Acta Math. 129 (1972), 137-193.
T. M. Flett, Temperatures, Bessel potentials and Lipschitz spaces, Proc. London Math. Soc. (3) 22 (1971), 385-451.
J. García-Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, Notas Mat. 116, North-Holland, Amsterdam, 1985.
I. I. Hirschman and D. V. Widder, The Convolution Transform, Princeton University Press, 1955.
E. Kochneff and Y. Sagher, Conjugate temperatures, J. Approx. Theory 70 (1992), 39-49.
S. Pérez-Esteva, Hardy spaces of vector-valued heat functions, Houston J. Math. 19 (1993), 127-134.
M. Riesz, L'intégrale de Riemann-Liouville et le problème de Cauchy, Acta Math. 81 (1949), 1-223.
E. M. Stein, Harmonic Analysis. Real-Variable Methods, Orthogonality and Oscillatory Integrals, Princeton University Press, 1993.
E. M. Stein and G. Weiss, On the theory of harmonic functions of several variables. I. The theory of $H^{p}$ spaces, Acta Math. 103 (1960), 25-62.

Title

Hardy spaces of conjugate temperatures

Affiliations

Abstract

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