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The two power-weight () norm inequalities for the Hilbert transform on the cones of monotone functions are characterized in the case 0 < p ≤ q < ∞.
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The research of the first author was partially supported by the Russian Fund for Basic Researches (Projects 09-01-00093, 09-01-00586, 10-01-91331). The research of the second author was partially supported by MTM 2008-05561-C02-02, 2009 SGR 1303, RFFI 09-01-00175, NSH-3252.2010.1.
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