Fine properties of functions from Hajłasz–Sobolev classes Mαp, p > 0, II. Lusin’s approximation
- Authors: Bondarev S.A.1, Krotov V.G.1
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Affiliations:
- Belarusian State University
- Issue: Vol 52, No 1 (2017)
- Pages: 30-37
- Section: Real and Complex Analysis
- URL: https://journals.rcsi.science/1068-3623/article/view/227993
- DOI: https://doi.org/10.3103/S1068362317010046
- ID: 227993
Cite item
Abstract
The present paper is devoted to the Lusin’s approximation of functions from Hajłasz–Sobolev classes Mαp(X) for p > 0. It is proved that for any f ∈ Mαp(X) and any ε > 0 there exist an open set Oε ⊂ X with measure less than ε (as a measure can be taken the corresponding capacity or Hausdorff content) and an approximating function fε such that f = fε on XOε. Moreover, the correcting function fε is regular (that is, it belongs to the underlying space Mαp(X) and it is a locally Hölder function), and it approximates the original function in the metric of the space Mαp(X).
About the authors
S. A. Bondarev
Belarusian State University
Author for correspondence.
Email: bsa0393@gmail.com
Belarus, Minsk
V. G. Krotov
Belarusian State University
Email: bsa0393@gmail.com
Belarus, Minsk