An uncertainty principle on the Lorentz spaces

Abstract

Via subtly combining the Plancherel theorem with various inequalities including Chebyshev’s inequality, generalized Hölder’s and Hausdorff–Young’s inequalities, we establish a new nonlinear uncertainty principle on the Lorentz spaces Lp,q(Rn) for whole ranges of the indexes p,q∈([1,∞)×(0,1])∪((1,∞)×(1,∞)).