An improvement of dimension-free Sobolev imbeddings in r spaces

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F14%3A00430335" target="_blank" >RIV/67985840:_____/14:00430335 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jfa.2014.04.011" target="_blank" >http://dx.doi.org/10.1016/j.jfa.2014.04.011</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jfa.2014.04.011" target="_blank" >10.1016/j.jfa.2014.04.011</a>

Result language
angličtina
Original language name
An improvement of dimension-free Sobolev imbeddings in r spaces
Original language description
We prove a dimension-invariant imbedding estimate for Sobolev spaces of first order into a small Lebesgue space, and we establish the optimality of its fundamental function. Namely, for any 1 < p < infinity, the inequality ||f*||Y-p(0,1) <= C-p ||del f||L-p(B-n) for all f is an element of W-0(1,p)(Bn), for all n > p (*) where Y-p(0, 1) is a rearrangement-invariant Banach function space independent of the dimension n, B-n is the ball in R-n of measure 1 and c(p) is a constant independent of n, is satisfied by the small Lebesgue space L-(p,L-p' /2(0, 1). Moreover, we show that the smallest space Y-p(0,1) (in the sense of the continuous imbedding) such that (*) is true has the fundamental function equivalent to that of L-(p,L-p'/2(0, 1). As a byproduct ofour results, we get that the space L-p (log L)(P/2) is optimal in the framework of the Orlicz spaces satisfying (*).
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GAP201%2F10%2F1920" target="_blank" >GAP201/10/1920: Contemporary function spaces theory and applications</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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