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On Tricomi's relation for the Hilbert transformation
Published online by Cambridge University Press: 18 May 2009
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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
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- Copyright © Glasgow Mathematical Journal Trust 1975