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Weighted norm inequalities for positive operators restricted on the cone of λ-quasiconcave functions

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    0522215 - MÚ 2021 RIV GB eng J - Článek v odborném periodiku
    Gogatishvili, Amiran - Neves, J. S.
    Weighted norm inequalities for positive operators restricted on the cone of λ-quasiconcave functions.
    Proceedings of the Royal Society of Edinburgh. A - Mathematics. Roč. 150, č. 1 (2020), s. 17-39. ISSN 0308-2105
    Grant CEP: GA ČR GA13-14743S
    Institucionální podpora: RVO:67985840
    Klíčová slova: quasilinear operator * integral inequality * Lebesgue space * Hardy operator * quasiconcave functions * monotone functions
    Kód oboru RIV: BA - Obecná matematika
    Obor OECD: Pure mathematics
    Impakt faktor: 1.045, rok: 2018
    https://doi.org/10.1017/prm.2018.85

    Let ρ be a monotone quasinorm de_ned on M^+, the set of all non-negative measurable functions on [0,1): Let T be a monotone quasilinear operator on M^+. We show that the following inequality restricted on the cone of λ-quasiconcave functions ρ(f)≤C(∫_0^∞ f^p v)^(1/p), where 1≤p≤∞ and v is a weighted function, is equivalent to slightly different inequalities consider for all non-negative measurable functions. The case 0 < p < 1 is also studied for quasinorms and operators with additional properties. These results in turn enables us to establish necessary and sufficient conditions on the weights (u, v,w) for which the three weighted Hardy-type inequalityholds for all ρ-quasiconcave functions and all 0 < p,q ≤∞.
    Trvalý link: http://hdl.handle.net/11104/0306710
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