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Mat. Zametki, 2017, Volume 102, Issue 4, Pages 514–525 (Mi mz11479)  

Finite-Dimensional Subspaces of $L_p$ with Lipschitz Metric Projection

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

Lomonosov Moscow State University

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.


DOI: https://doi.org/10.4213/mzm11479

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English version:
Mathematical Notes, 2017, 102:4, 465–474

Bibliographic databases:

Document Type: Article
UDC: 517.982.256
Received: 04.12.2016

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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