On grand and small Lebesgue and Sobolev spaces and some applications to PDEs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F18%3A00486954" target="_blank" >RIV/67985840:_____/18:00486954 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.7153/dea-2018-10-03" target="_blank" >http://dx.doi.org/10.7153/dea-2018-10-03</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.7153/dea-2018-10-03" target="_blank" >10.7153/dea-2018-10-03</a>

Result language
angličtina
Original language name
On grand and small Lebesgue and Sobolev spaces and some applications to PDEs
Original language description
This paper is essentially a survey on grand and small Lebesgue spaces, which arerearrangement-invariant Banach function spaces of interest not only from the point of view of Function Spaces theory, but also from the point of view of their applications: the corresponding Sobolev spaces are of interest, for instance, in the theory of PDEs. We discuss results of existence, uniqueness and regularity of certain Dirichlet problems, where the knowledge of these spaces plays a central role. The novelty of this paper relies in an unified treatment containing a number of equivalent quasinorms, all written making explicit the dependence of |omega|, in the discussion of the sharpness of Hölder’s inequality, and in the connection of the results in PDEs with some existing literature.
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/GA13-14743S" target="_blank" >GA13-14743S: Function spaces, weighted inequalities and interpolation II</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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