Some new Two-Sided Inequalities concerning the Fourier Transform
The classical Hausdorff-Young and Hardy-Littlewood-Stein inequalities do not hold for p > 2. In this paper we prove that if we restrict to net spaces we can even derive a two-sided estimate for all p > 1. In particular, this result generalizes a recent result by Liflyand E. and Tikhonov S.  (MR 2464253).
OAD program http://mia.ele-math.com/open-access-on-demand Article published under the CCANCL terms. Link to publisher's version: http://mia.ele-math.com/20-54/Some-new-two-sided-inequalities-concerning-the-Fourier-transform