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2009
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We study norm convolution inequalities in Lebesgue and Lorentz spaces. First, we improve the well-known O'Neil's inequality for the convolution operators and prove corresponding estimate from below. Second, we obtain Young–O'Neil-type estimate in the Lorentz spaces for the limit value parameters, i.e., ‖ K ∗ f ‖ L ( p , h 1 ) → L ( p , h 2 ) . Finally, similar estimates in the weighted Lorentz spaces are presented.