Gagliardo-Nirenberg Inequality for rearrangement-invariant Banach function spaces
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60076658%3A12510%2F19%3A43899530" target="_blank" >RIV/60076658:12510/19:43899530 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21240/19:00339283
Result on the web
<a href="https://www.ems-ph.org/journals/show_abstract.php?issn=1120-6330&vol=30&iss=4&rank=7" target="_blank" >https://www.ems-ph.org/journals/show_abstract.php?issn=1120-6330&vol=30&iss=4&rank=7</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4171/RLM/872" target="_blank" >10.4171/RLM/872</a>
Alternative languages
Result language
angličtina
Original language name
Gagliardo-Nirenberg Inequality for rearrangement-invariant Banach function spaces
Original language description
The classical Gagliardo-Nirenberg interpolation inequality is a well-known estimate which gives, in particular, an estimate for the Lebesgue norm of intermediate derivatives of functions in Sobolev spaces. We present an extension of this estimate into the scale of the general rearrangement-invariant Banach function spaces with the proof based on the Maz'ya's pointwise estimates. As corollaries, we present the Gagliardo-Nirenberg inequality for intermediate derivatives in the case of triples of Orlicz spaces and triples of Lorentz spaces. Finally, we promote the scaling argument to validate the optimality of the Gagliardo-Nirenberg inequality and show that the presented estimate in Orlicz scale is optimal.
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/GJ18-00960Y" target="_blank" >GJ18-00960Y: Selected topics in non-linear functional analysis and approximation theory</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Rendiconti Lincei - Matematica e Applicazioni
ISSN
1120-6330
e-ISSN
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Volume of the periodical
30
Issue of the periodical within the volume
4
Country of publishing house
CH - SWITZERLAND
Number of pages
18
Pages from-to
847-864
UT code for WoS article
000495622900007
EID of the result in the Scopus database
2-s2.0-85076801591