Abstract
Via subtly combining the Plancherel theorem with various inequalities including Chebyshevâs inequality, generalized Hölderâs and HausdorffâYoungâs inequalities, we establish a new nonlinear uncertainty principle on the Lorentz spaces Lp,q(Rn) for whole ranges of the indexes p,qâ([1,â)Ă(0,1])âȘ((1,â)Ă(1,â)).
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