Discretization and antidiscretization of Lorentz norms with no restrictions on weights
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10441250" target="_blank" >RIV/00216208:11320/21:10441250 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21230/22:00359331
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=ZwUtOKtd7B" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=ZwUtOKtd7B</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s13163-021-00399-7" target="_blank" >10.1007/s13163-021-00399-7</a>
Alternative languages
Result language
angličtina
Original language name
Discretization and antidiscretization of Lorentz norms with no restrictions on weights
Original language description
We improve the discretization technique for weighted Lorentz norms by eliminating all “non-degeneracy” restrictions on the involved weights. We use the new method to provide equivalent estimates on the optimal constant C such that the inequality (∫0L(f∗(t))qw(t)dt)1q≤C(∫0L(∫0tu(s)ds)-p(∫0tf∗(s)u(s)ds)pv(t)dt)1pholds for all relevant measurable functions, where L∈ (0 , ∞] , p, q∈ (0 , ∞) and u, v, w are locally integrable weights, u being strictly positive. In the case of weights that would be otherwise excluded by the restrictions, it is shown that additional limit terms naturally appear in the characterizations of the optimal C. A weak analogue for p= ∞ is also presented.
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
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)
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Revista Matematica Complutense
ISSN
1139-1138
e-ISSN
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Volume of the periodical
2021
Issue of the periodical within the volume
6
Country of publishing house
ES - SPAIN
Number of pages
34
Pages from-to
1-34
UT code for WoS article
000664410600001
EID of the result in the Scopus database
2-s2.0-85108697143