Hardy spaces of conjugate temperatures

Martha Guzmán-Partida

Studia Mathematica (1997)

  • Volume: 122, Issue: 2, page 153-165
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Guzmán-Partida, Martha. "Hardy spaces of conjugate temperatures." Studia Mathematica 122.2 (1997): 153-165. <http://eudml.org/doc/216367>.

@article{Guzmán1997,
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.},
author = {Guzmán-Partida, Martha},
journal = {Studia Mathematica},
keywords = {Hardy spaces; conjugate temperatures},
language = {eng},
number = {2},
pages = {153-165},
title = {Hardy spaces of conjugate temperatures},
url = {http://eudml.org/doc/216367},
volume = {122},
year = {1997},
}

TY - JOUR
AU - Guzmán-Partida, Martha
TI - Hardy spaces of conjugate temperatures
JO - Studia Mathematica
PY - 1997
VL - 122
IS - 2
SP - 153
EP - 165
AB - 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.
LA - eng
KW - Hardy spaces; conjugate temperatures
UR - http://eudml.org/doc/216367
ER -

References

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  1. [1] H. S. Bear, Hardy spaces of heat functions, Trans. Amer. Math. Soc. 301 (1987), 831-844. Zbl0633.31002
  2. [2] J. R. Cannon, The One-Dimensional Heat Equation, Encyclopedia Math. Appl. 23, Addison-Wesley, 1984. 
  3. [3] C. Fefferman and E. M. Stein, H p spaces of several variables, Acta Math. 129 (1972), 137-193. Zbl0257.46078
  4. [4] T. M. Flett, Temperatures, Bessel potentials and Lipschitz spaces, Proc. London Math. Soc. (3) 22 (1971), 385-451. 
  5. [5] J. García-Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, Notas Mat. 116, North-Holland, Amsterdam, 1985. 
  6. [6] I. I. Hirschman and D. V. Widder, The Convolution Transform, Princeton University Press, 1955. Zbl0039.33202
  7. [7] E. Kochneff and Y. Sagher, Conjugate temperatures, J. Approx. Theory 70 (1992), 39-49. 
  8. [8] S. Pérez-Esteva, Hardy spaces of vector-valued heat functions, Houston J. Math. 19 (1993), 127-134. Zbl0806.46036
  9. [9] M. Riesz, L'intégrale de Riemann-Liouville et le problème de Cauchy, Acta Math. 81 (1949), 1-223. 
  10. [10] E. M. Stein, Harmonic Analysis. Real-Variable Methods, Orthogonality and Oscillatory Integrals, Princeton University Press, 1993. Zbl0821.42001
  11. [11] 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. Zbl0097.28501

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