Email this article Finite-dimensional subspaces of Lp with Lipschitz metric projection
- Authors: Borodin P.A.1, Druzhinin Y.Y.1, Chesnokova K.V.1
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Affiliations:
- Lomonosov Moscow State University
- Issue: Vol 102, No 3-4 (2017)
- Pages: 465-474
- Section: Article
- URL: https://journal-vniispk.ru/0001-4346/article/view/150139
- DOI: https://doi.org/10.1134/S0001434617090188
- ID: 150139
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Abstract
We prove that the metric projection onto a finite-dimensional subspace Y ⊂ Lp, p ∈ (1, 2) ∪ (2, ∞), 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.
About the authors
P. A. Borodin
Lomonosov Moscow State University
Author for correspondence.
Email: pborodin@inbox.ru
Russian Federation, Moscow
Yu. Yu. Druzhinin
Lomonosov Moscow State University
Email: pborodin@inbox.ru
Russian Federation, Moscow
K. V. Chesnokova
Lomonosov Moscow State University
Email: pborodin@inbox.ru
Russian Federation, Moscow
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