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Matematicheskie Zametki, 2017, Volume 102, Issue 4, Pages 514–525
DOI: https://doi.org/10.4213/mzm11479 (Mi mzm11479) 		 
Finite-Dimensional Subspaces of $L_p$ with Lipschitz Metric Projection

P. A. Borodin, Yu. Yu. Druzhinin, K. V. Chesnokova

Lomonosov Moscow State University
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DOI: https://doi.org/10.4213/mzm11479
Abstract: We prove that the metric projection onto a finite-dimensional subspace $Y\subset L_p$, $p\in(1,2)\cup(2,\infty)$, satisfies the Lipschitz condition if and only if every function in $Y$ is supported on finitely many atoms. We estimate the Lipschitz constant of such a projection for the case in which the subspace is one-dimensional.
Keywords: metric projection, Lipschitz condition, $L_p$ space, linearity coefficient.
Funding agency Grant number
Russian Foundation for Basic Research 15-01-08335
Dynasty Foundation
The work of all the authors was supported by the Russian Foundation for Basic Research under grant no. 15-01-08335. The first author's work was supported by Dmitry Zimin's “Dynasty” foundation.
Received: 04.12.2016
English version:
Mathematical Notes, 2017, Volume 102, Issue 4, Pages 465–474
DOI: https://doi.org/10.1134/S0001434617090188
Bibliographic databases:
Document Type: Article
UDC: 517.982.256
Language: Russian
Citation: P. A. Borodin, Yu. Yu. Druzhinin, K. V. Chesnokova, “Finite-Dimensional Subspaces of $L_p$ with Lipschitz Metric Projection”, Mat. Zametki, 102:4 (2017), 514–525; Math. Notes, 102:4 (2017), 465–474
Citation in format AMSBIB
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\pages 514--525
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