Abstract
Suppose and
. Let
be an α-harmonic mapping on
with the boundary F being absolute continuous and
, where
. In this paper, we investigate the membership of
and
in the space
, the generalized Hardy space. We prove, if
, then both
and
are in
. If
, then
and
if and only if f is analytic. Finally, we investigate a Schwarz Lemma for α-harmonic functions.
AMS Subject Classifications:
Acknowledgments
The authors would like to thank the referees for insightful comments which led to significant improvements in the paper. A special thanks to a referee for proving us with an elementary proof of Lemma 3.2.
Disclosure statement
No potential conflict of interest was reported by the author(s).