Nagata dimension and Lipschitz extensions into quasi-Banach spaces

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10511047" target="_blank" >RIV/00216208:11320/25:10511047 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=RlpVQUJtBk" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=RlpVQUJtBk</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4064/sm240416-12-3" target="_blank" >10.4064/sm240416-12-3</a>

Result language
angličtina
Original language name
Nagata dimension and Lipschitz extensions into quasi-Banach spaces
Original language description
Given two metric spaces N subset of M and 0 < p < 1, we wish to determine the smallest constant t(p)(N, M) such that any Lipschitz map f : N - Z into any pBanach space Z can be extended to a Lipschitz map f ' : M - Z satisfying Lip f ' < t(p)(N, M) center dot Lip f. We prove that if N has finite Nagata dimension at most d with constant gamma, then t(p)(N, M) less than or similar to p gamma center dot (d + 1)(1/p-1 )center dot log(d + 2) for all 0 < p < 1. We show that examples of spaces with finite Nagata dimension include doubling spaces, as well as minor-excluded metric graphs. We also establish that the constant t(p)(N, M) generally increases as p approaches zero.
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
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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