Weighted inequalities for iterated Copson integral operators

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10421889" target="_blank" >RIV/00216208:11320/20:10421889 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=DTYEzR26aW" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=DTYEzR26aW</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4064/sm181016-5-5" target="_blank" >10.4064/sm181016-5-5</a>

Result language
angličtina
Original language name
Weighted inequalities for iterated Copson integral operators
Original language description
We solve a long-standing open problem in the theory of weighted inequalities concerning iterated Copson operators. We use a constructive approximation method based on a new discretization principle. As a result, we characterize all weight functions w; v; u on (0,infinity) for which there exists a constant C such that the inequality (integral(infinity)(0)(integral(infinity)(t)(integral(infinity)(s)h(y)dy)(m) u(s)ds)(q/m)omega(t)dt)(1/q) <= C(integral(infinity)(0) h(t)(p)v(t)dt)(1/p) holds for every non-negative measurable function h on (0,infinity), where p,q and m are positive parameters. We assume that p >= 1 because otherwise the inequality cannot hold for non-trivial weights, but otherwise p,q and m are unrestricted.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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