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Weighted norm inequalities for positive operators restricted on the cone of λ-quasiconcave functions
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SYSNO ASEP 0522215 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Weighted norm inequalities for positive operators restricted on the cone of λ-quasiconcave functions Author(s) Gogatishvili, Amiran (MU-W) RID, ORCID, SAI
Neves, J. S. (PT)Source Title Proceedings of the Royal Society of Edinburgh. A - Mathematics. - : Royal Society of Edinburgh - ISSN 0308-2105
Roč. 150, č. 1 (2020), s. 17-39Number of pages 23 s. Language eng - English Country GB - United Kingdom Keywords quasilinear operator ; integral inequality ; Lebesgue space ; Hardy operator ; quasiconcave functions ; monotone functions Subject RIV BA - General Mathematics OECD category Pure mathematics R&D Projects GA13-14743S GA ČR - Czech Science Foundation (CSF) Method of publishing Open access Institutional support MU-W - RVO:67985840 UT WOS 000513240300002 EID SCOPUS 85060378432 DOI 10.1017/prm.2018.85 Annotation 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 ≤∞. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2021 Electronic address https://doi.org/10.1017/prm.2018.85
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