Embeddings of homogeneous Sobolev spaces on the entire space

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10441248" target="_blank" >RIV/00216208:11320/21:10441248 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=lJJYWdMOE" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=lJJYWdMOE</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/prm.2020.14" target="_blank" >10.1017/prm.2020.14</a>

Result language
angličtina
Original language name
Embeddings of homogeneous Sobolev spaces on the entire space
Original language description
We completely characterize the validity of the inequality parallel to u parallel to(Y(Rn)) <= C parallel to del(m)u parallel to(X(Rn)), where X and Y are rearrangement-invariant spaces, by reducing it to a considerably simpler one-dimensional inequality. Furthermore, we fully describe the optimal rearrangement-invariant space on either side of the inequality when the space on the other side is fixed. We also solve the same problem within the environment in which the competing spaces are Orlicz spaces. A variety of examples involving customary function spaces suitable for applications is also provided.
Czech name
—
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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