RUS  ENG
Full version
JOURNALS // Matematicheskie Zametki // Archive

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

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.

UDC: 517.982.256

Received: 04.12.2016

DOI: 10.4213/mzm11479


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

Bibliographic databases:


© Steklov Math. Inst. of RAS, 2025