Author： BUCˇKOVSKA A.L.
Publisher： Taylor & Francis Ltd
ISSN： 1065-2469
Source： Integral Transforms and Special Functions, Vol.13, Iss.1, 2002-01, pp. : 1-15
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Abstract
The bilinear Hilbert transform <$>H_{alpha}colon L^2times L^infty rightarrow L^2<$> respectively, <$>H_{alpha}colon L^{p_1}times L^{p_2} rightarrow L^{p}<$>, is extended to <$>{cal D}_{L^2}^primetimes {cal D}_{L^infty}rightarrow <$> <$>{cal D}_{L^2}^prime<$>, respectively, <$>{cal D}_{L^q}^primetimes {cal D}_{L^{p_2}} rightarrow {cal D}_{q_1}^prime<$>, (with suitable parameters) as a hypocontinuous, respectively, continuous mapping. The bilinear Hilbert transform of Schwartz distributions is defined as an irregular operation. The inversion formula is given. It is used as a product formula for appropriate pairs of distributions.
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