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Approximation and Quasicontinuity of Besov and Triebel–Lizorkin Functions

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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
Published in
Transactions of the American Mathematical Society
Authors
Heikkinen, Toni |
Koskela, Pekka |
Tuominen, Heli
Date
2017
Discipline
MatematiikkaMathematics
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.

 
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 Society
ISSN Search the Publication Forum
0002-9947
Keywords
Besov space Triebel–Lizorkin space fractional Sobolev space metric measure space median quasicontinuity

Original source
http://www.ams.org/journals/tran/0000-000-00/S0002-9947-2016-06886-5/S0002-9947-2016-06886-5.pdf

DOI
https://doi.org/10.1090/tran/6886
URI

http://urn.fi/URN:NBN:fi:jyu-201702131428

Publication in research information system

https://converis.jyu.fi/converis/portal/detail/Publication/26415576

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