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A NEW GENERALIZATION OF BOAS THEOREM FOR SOME LORENTZ SPACES Λq(ω)
(Journal article; Tidsskriftartikkel; Peer reviewed, 2018)
Let Λq( ω ), q > 0, denote the Lorentz space equipped with the (quasi) norm [<i>MATHEMATICAL FORMULA</I>] for a function f on [0,1] and with ω positive and equipped with some additional growth properties. A generalization of Boas theorem in the form of a two-sided inequality is obtained in the case of both general regular system [<i>MATHEMATICAL FORMULA</I>] and generalized Lorentz Λq( ω ) spaces
Some new Two-Sided Inequalities concerning the Fourier Transform
(Journal article; Peer reviewed; Tidsskriftartikkel, 2017)
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).