Inequalities in fourier analysis on R.
THIS NOTE DESCRIBES TWO RESULTS: (i) a sharp Hausdorff-Young inequality for the Fourier transform on L(p)(R(n)) which extends an earlier result of Babenko; and (ii) a sharp form of Young's inequality for the convolution of functions on R(n). That is, best possible constants are obtained for the following L(p)(R(n)) inequalities: [Formula: see text].
Beckner
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Department of Mathematics, Princeton University, Princeton, New Jersey 08540.