Poincaré-Sobolev inequalities with rearrangement-invariant norms on the entire space

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10441251" target="_blank" >RIV/00216208:11320/21:10441251 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=lKFrN-6Y5f" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=lKFrN-6Y5f</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00209-020-02652-z" target="_blank" >10.1007/s00209-020-02652-z</a>

Result language
angličtina
Original language name
Poincaré-Sobolev inequalities with rearrangement-invariant norms on the entire space
Original language description
Poincaré-Sobolev-type inequalities involving rearrangement-invariant norms on the entire Rn are provided. Namely, inequalities of the type ‖u-P‖Y(Rn)≤C‖∇mu‖X(Rn), where X and Y are either rearrangement-invariant spaces over Rn or Orlicz spaces over Rn, u is a m- times weakly differentiable function whose gradient is in X, P is a polynomial of order at most m- 1 , depending on u, and C is a constant independent of u, are studied. In a sense optimal rearrangement-invariant spaces or Orlicz spaces Y in these inequalities when the space X is fixed are found. A variety of particular examples for customary function spaces are also provided.
Czech name
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Czech description
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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

Project
<a href="/en/project/GA18-00580S" target="_blank" >GA18-00580S: Function Spaces and Approximation</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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