Abstract:
For $H^p$ functions in the unit disc, $0<p\le1$, it is shown
that the rate of approximation of the boundary function in the $L^p$ metric
by the generalized Riesz means
$R_\varepsilon^{l,\alpha}(f,z)$, $\varepsilon>0$,
$(l+1)p>1$, $(\alpha+1)p>1$, is equivalent to the modulus of
smoothness of fractional order $l$.
This is a known result in the case of positive integer $l$.
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