Geodesic
On Tricomi's relation for the Hilbert transformation
Glasgow mathematical journal, Tome 16 (1975) no. 1, pp. 52-56

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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 iswhere the symbol (P) denotes that the integral is taken in the Cauchy principal value sense, then 
Rooney, P. G. On Tricomi's relation for the Hilbert transformation. Glasgow mathematical journal, Tome 16 (1975) no. 1, pp. 52-56. doi: 10.1017/S0017089500002500
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[1] 1.Titchmarsh, E. C., Theory of Fourier integrals, Second Edition (Oxford, 1948). Google Scholar

[2] 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). Google Scholar | DOI

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