Optimality problems in Orlicz spaces
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10475499" target="_blank" >RIV/00216208:11320/23:10475499 - isvavai.cz</a>
Alternative codes found
RIV/00216224:14330/23:00133451
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=KPoXo77ASj" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=KPoXo77ASj</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.aim.2023.109273" target="_blank" >10.1016/j.aim.2023.109273</a>
Alternative languages
Result language
angličtina
Original language name
Optimality problems in Orlicz spaces
Original language description
In mathematical modelling, the data and solutions are represented as measurable functions and their quality is oftentimes captured by the membership to a certain function space. One of the core questions for an analysis of a model is the mutual relationship between the data and solution quality. The optimality of the obtained results deserves aspecial focus. It requires acareful choice of families of function spaces balancing between their expressivity, i.e. the ability to capture fine properties of the model, and their accessibility, i.e. its technical difficulty for practical use. This paper presents aunified and general approach to optimality problems in Orlicz spaces. Orlicz spaces are parametrized by a single convex function and neatly balance the expressivity and accessibility. We prove a general principle that yields an easily verifiable necessary and sufficient condition for the existence or the non-existence of an optimal Orlicz space in various tasks. We demonstrate its use in specific problems, including the continuity of Sobolev embeddings and boundedness of integral operators such as the Hardy-Littlewood maximal operator and the Laplace transform.
Czech name
—
Czech description
—
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/EF18_053%2F0016952" target="_blank" >EF18_053/0016952: Postdoc2MUNI</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
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
Advances in Mathematics
ISSN
0001-8708
e-ISSN
1090-2082
Volume of the periodical
2023
Issue of the periodical within the volume
432
Country of publishing house
US - UNITED STATES
Number of pages
58
Pages from-to
1-58
UT code for WoS article
001078404400001
EID of the result in the Scopus database
2-s2.0-85171149845