Optimal Gagliardo-Nirenberg interpolation inequality for rearrangement invariant spaces
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F23%3A50020730" target="_blank" >RIV/62690094:18470/23:50020730 - isvavai.cz</a>
Alternative codes found
RIV/60076658:12410/23:43906613 RIV/46747885:24510/23:00011278
Result on the web
<a href="https://link.springer.com/article/10.1007/s13398-023-01481-z" target="_blank" >https://link.springer.com/article/10.1007/s13398-023-01481-z</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s13398-023-01481-z" target="_blank" >10.1007/s13398-023-01481-z</a>
Alternative languages
Result language
angličtina
Original language name
Optimal Gagliardo-Nirenberg interpolation inequality for rearrangement invariant spaces
Original language description
We prove the optimality of the Gagliardo-Nirenberg inequality: parallel to del u parallel to X less than or similar to parallel to del(2)u parallel to(12)(Y)parallel to u parallel to(12)(Z), where Y and Z are rearrangement invariant Banach function spaces, and X = Y(1/2)Z(1/2) is the Calderon-Lozanovskii space. By optimality, we mean that for a certain pair of spaces on the right-hand side, it is not possible to reduce the space on the left-hand side while remaining in the class of rearrangement invariant spaces. Our result establishes the optimality for Lorentz and Orlicz spaces, surpassing previous findings. Additionally, we discuss the significance of pointwise inequalities and present a counterexample that prohibits further improvements.
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
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GJ20-19018Y" target="_blank" >GJ20-19018Y: Delicate analytical and topological tools for variational problems and modelling</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
ISSN
1578-7303
e-ISSN
1579-1505
Volume of the periodical
117
Issue of the periodical within the volume
4
Country of publishing house
IT - ITALY
Number of pages
23
Pages from-to
"Article Number: 161"
UT code for WoS article
001057705100001
EID of the result in the Scopus database
2-s2.0-85168801372