Approximation and Quasicontinuity of Besov and Triebel–Lizorkin Functions
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
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Transactions of the American Mathematical SocietyDate
2017Copyright
© 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.
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.
Publisher
American Mathematical SocietyISSN Search the Publication Forum
0002-9947Keywords
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http://www.ams.org/journals/tran/0000-000-00/S0002-9947-2016-06886-5/S0002-9947-2016-06886-5.pdfPublication in research information system
https://converis.jyu.fi/converis/portal/detail/Publication/26415576
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