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Abstract

The classical H p spaces are defined for 0 < p < ∞ to consist of those functions f, holomorphic in the right half-plane, with the property that µ p(f, x) is bounded for x>0, where
$$ {\mu _p}(f,x) = {\left\{ {\frac{1} {{2\pi }}\int\limits_{ - \infty }^\infty {\left| {f{{(x + iy)}^p}dy} \right|} } \right\}^{1/p}} $$
(1.1)
.

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References

  1. [1]
    G. Doetsch, Bedingungen für die Darstellbarkeit einer Funktion als Laplace-Integral und eine Umkehrformel für die Laplace-Transformation. Math. Z. 42 (1937), 263–286.CrossRefGoogle Scholar
  2. [2]
    R. E. Edwards, Fourier Series II. Holt, Rinehart and Winston, New York 1967.Google Scholar
  3. [3]
    P. G. Rooney, On some properties of functions analytic in half-plane. Can. J. Math. 11 (1959), 432–439.CrossRefGoogle Scholar
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    P. G. Rooney, A generalization of the Hardy spaces. Can. J. Math. 16 (1964), 358–369.CrossRefGoogle Scholar
  5. [5]
    E. C. Titchmarsh, An introduction to the theory of Fourier integrals. Clarendon Press, Oxford 1948.Google Scholar

Copyright information

© Springer Basel AG 1969

Authors and Affiliations

  • P. G. Rooney
    • 1
  1. 1.University of TorontoCanada

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