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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