Approximation and Quasicontinuity of Besov and Triebel–Lizorkin Functions
Finna-arvio
Approximation and Quasicontinuity of Besov and Triebel–Lizorkin Functions
www.ams.org/journals...-06886-5.pdf
(Jyväskylän yliopisto - JYX / artikkelit)
heikkinenkoskelatuominenapproximation.pdf
(Jyväskylän yliopisto - JYX / artikkelit)
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.
Tallennettuna:
Kieli |
englanti |
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Sarja | Transactions of the American Mathematical Society, 5 |
Aiheet | |
ISSN |
0002-9947 |