It is proved that certain convolution inequalities are easy consequences of the Hardy-Littlewood-Wiener maximal theorem. These inequalities include the Hardy-Littlewood-Sobolev inequality for fractional integrals, its extension by Trudinger, and an interpolation inequality by Adams and Meyers. We also improve a recent extension of Trudingerâs inequality due to Strichartz.
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Lars Inge Hedberg (1972) studied this question.