Approximation and Quasicontinuity of Besov and Triebel–Lizorkin Functions
Abstract
We show that, for 0 < s < 1, 0 < p, q < ∞, Haj lasz–Besov and
Haj lasz–Triebel–Lizorkin functions can be approximated in the norm by discrete
median convolutions. This allows us to show that, for these functions, the limit
of medians,
lim
r→0
mγ
u
(B(x, r)) = u
∗
(x),
exists quasieverywhere and defines a quasicontinuous representative of u. The
above limit exists quasieverywhere also for Haj lasz functions u ∈ Ms,p, 0 < s ≤ 1,
0 < p < ∞, but approximation of u in Ms,p by discrete (median) convolutions is
not in general possible.
Main Authors
Format
Articles
Research article
Published
2017
Series
Subjects
Publication in research information system
Publisher
American Mathematical Society
Original source
http://www.ams.org/journals/tran/0000-000-00/S0002-9947-2016-06886-5/S0002-9947-2016-06886-5.pdf
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-201702131428Use this for linking
Review status
Peer reviewed
ISSN
0002-9947
DOI
https://doi.org/10.1090/tran/6886
Language
English
Published in
Transactions of the American Mathematical Society
Citation
- Heikkinen, T., Koskela, P., & Tuominen, H. (2017). Approximation and Quasicontinuity of Besov and Triebel–Lizorkin Functions. Transactions of the American Mathematical Society, 369(5), 3547-3573. https://doi.org/10.1090/tran/6886
License
Copyright© 2016 American Mathematical Society. This is a final draft version of an article whose final and definitive form has been published by AMS. Published in this repository with the kind permission of the publisher.