Hostname: page-component-76fb5796d-25wd4 Total loading time: 0 Render date: 2024-04-26T10:42:46.640Z Has data issue: false hasContentIssue false
  • English
  • Français

A Generalization of the Hardy Spaces

Published online by Cambridge University Press:  20 November 2018

P. G. Rooney
P. G. Rooney*
Affiliation:
University of Toronto
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 Hardy spaces for right half-planes, , σ real, 1 ≤ p ≤ ∞, are defined to consist of all those functions f(s), holomorphic for Re s > σ, for which μp(f, x) exists and is bounded for x > σ, where

These spaces have been studied extensively (see, for example, 3, Chapter 8, and 2, §19.1).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 16 , 1964 , pp. 358 - 369
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Doetsch, G., Bedingungen fur die Darstellbarkeit einer Funktion als Laplace-Integral und eine Umkehrformel fur die Laplace-Transformation, Math. Z., 42 (1937), 263–286.Google Scholar
2. Hille, E., Analytic function theory, II (New York, 1962).Google Scholar
3. Hoffman, K., Banach spaces of analytic functions (Englewood Cliffs, N.J., 1962).Google Scholar
4. Paley, R. E. A. C. and Wiener, N., Fourier transforms in the complex domain (New York, 1934).Google Scholar
5. Rooney, P. G., On some theorems of Doetsch, Can. J. Math., 10 (1958), 421–430.Google Scholar
6. Shohat, J., Laguerre polynomials and the Laplace transform, Duke Math. ]., 6 (1940), 615– 626.Google Scholar
7. Titchmarsh, E. C., Introduction to the theory of Fourier integrals (Oxford, 1948).Google Scholar
8. Widder, D. V., The Laplace transform (Princeton, 1941).Google Scholar