Abstract
We show that, for 0 < s < 1, 0 < p < ∞, 0 < q < ∞, Hajłasz–Besov and Hajłasz–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, [Formula Presented] exists quasieverywhere and defines a quasicontinuous representative of u. The above limit exists quasieverywhere also for Hajłasz 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.
Original language | English |
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Pages (from-to) | 3547-3573 |
Number of pages | 27 |
Journal | Transactions of the American Mathematical Society |
Volume | 369 |
Issue number | 5 |
DOIs | |
Publication status | Published - 2017 |
MoE publication type | A1 Journal article-refereed |
Keywords
- Besov space
- Fractional Sobolev space
- Median
- Metric measure space
- Quasicontinuity
- Triebel–Lizorkin space