On the volume of unit balls of finite-dimensional Lorentz spaces

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10414142" target="_blank" >RIV/00216208:11320/20:10414142 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21340/20:00343525
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=vjM~4xPKve" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=vjM~4xPKve</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jat.2020.105407" target="_blank" >10.1016/j.jat.2020.105407</a>

Result language
angličtina
Original language name
On the volume of unit balls of finite-dimensional Lorentz spaces
Original language description
We study the volume of unit balls B-p,q(n) of finite-dimensional Lorentz sequence spaces l(p,q)(n). We give an iterative formula for vol(B-p,q(n)) for the weak Lebesgue spaces with q = infinity and explicit formulas for q = 1 and q = infinity. We derive asymptotic results for the nth root of vol(B-p,q(n)) and show that [vol(B-p,q(n)](1/n) asymptotic to(p,q) n(-1/p) for all 0 < p < infinity and 0 < q <= infinity. We study further the ratio between the volume of unit balls of weak Lebesgue spaces and the volume of unit balls of classical Lebesgue spaces. We conclude with an application of the volume estimates and characterize the decay of the entropy numbers of the embedding of the weak Lebesgue space l(p),(n)(infinity) into l(p)(n). (C) 2020 Elsevier Inc. All rights reserved.
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
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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