APPROXIMATION AND QUASICONTINUITY OF BESOV AND TRIEBEL LIZORKIN FUNCTIONS

We show that, for 0 < s < 1, 0 < p < infinity, 0 < q < infinity, Hajlasz-Besov and Hajlasz-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) m(u)(gamma)(B(x, r)) = u*(x), exists quasieverywhere and defines a quasicontinuous representative of u. The above limit exists quasieverywhere also for Hajlasz functions u epsilon M-s,M-p, 0 < s <= 1, 0 < p < infinity, but approximation of u in M-s,M-p by discrete (median) convolutions is not in general possible.