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Sobolev embeddings, rearrangement-invariant spaces and Frostman measures

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10421886" target="_blank" >RIV/00216208:11320/20:10421886 - isvavai.cz</a>

  • Result on the web

    <a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=r9R0e-xEQZ" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=r9R0e-xEQZ</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1016/j.anihpc.2019.06.004" target="_blank" >10.1016/j.anihpc.2019.06.004</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Sobolev embeddings, rearrangement-invariant spaces and Frostman measures

  • Original language description

    Sobolev embeddings, of arbitrary order, are considered into function spaces on domains of R-n endowed with measures whose decay on balls is dominated by a power d of their radius. Norms in arbitrary rearrangement-invariant spaces are contemplated. A comprehensive approach is proposed based on the reduction of the relevant n-dimensional embeddings to one-dimensional Hardy-type inequalities. Interestingly, the latter inequalities depend on the involved measure only through the power d. Our results allow for the detection of the optimal target space in Sobolev embeddings, for broad families of norms, in situations where customary techniques do not apply. In particular, new embeddings, with augmented target spaces, are deduced even for standard Sobolev spaces. (C) 2019 Elsevier Masson SAS. All rights reserved.

  • 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

  • Continuities

    I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2020

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    Annales de l&apos;Institut Henri Poincaré C, Analyse Non Linéaire

  • ISSN

    0294-1449

  • e-ISSN

  • Volume of the periodical

    37

  • Issue of the periodical within the volume

    1

  • Country of publishing house

    FR - FRANCE

  • Number of pages

    40

  • Pages from-to

    105-144

  • UT code for WoS article

    000510532500005

  • EID of the result in the Scopus database

    2-s2.0-85074485591