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On Tricomi's relation for the Hilbert transformation

Published online by Cambridge University Press:  18 May 2009

P. G. Rooney
P. G. Rooney
Affiliation:
University of Toronto
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Tricomi [2] has shown that if φi ∈ Lpi (− ∞, ∞), i = 1, 2, where 1 < pi < ∞, (pi)–l + (P2)–1 < 1, and if H denotes the Hilbert transformation, that is

where the symbol (P) denotes that the integral is taken in the Cauchy principal value sense, then

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 16 , Issue 1 , March 1975 , pp. 52 - 56
Copyright
Copyright © Glasgow Mathematical Journal Trust 1975

References

REFERENCES

1.Titchmarsh, E. C., Theory of Fourier integrals, Second Edition (Oxford, 1948).Google Scholar
2.Tricomi, F. G., On the finite Hilbert transformation, Quart. J. Math. (2) 2, 1951, 199–211 (see also F. G. Tricomi, Integral equations, Interscience Publ. (New York, 1957), § 4.3).CrossRefGoogle Scholar