Weighted norm inequalities for positive operators restricted on the cone of λ-quasiconcave functions
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F20%3A00522215" target="_blank" >RIV/67985840:_____/20:00522215 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1017/prm.2018.85" target="_blank" >https://doi.org/10.1017/prm.2018.85</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/prm.2018.85" target="_blank" >10.1017/prm.2018.85</a>
Alternative languages
Result language
angličtina
Original language name
Weighted norm inequalities for positive operators restricted on the cone of λ-quasiconcave functions
Original language description
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 ≤∞.
Czech name
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Czech description
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Classification
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
Result continuities
Project
<a href="/en/project/GA13-14743S" target="_blank" >GA13-14743S: Function spaces, weighted inequalities and interpolation II</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Proceedings of the Royal Society of Edinburgh. A - Mathematics
ISSN
0308-2105
e-ISSN
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Volume of the periodical
150
Issue of the periodical within the volume
1
Country of publishing house
GB - UNITED KINGDOM
Number of pages
23
Pages from-to
17-39
UT code for WoS article
000513240300002
EID of the result in the Scopus database
2-s2.0-85060378432