![Sample our Computer Science journals, sign in here to start your access, latest two full volumes FREE to you for 14 days]({"type":"image" , "src" : "/sda/5928/TOC-Subject-Sample-2021-Computer-Science.jpg"})
Abstract
Let be the family of analytic functions on
. Let
be an analytic self-map of
and
for
. Let
be the weighted composition operator on
. It is proved that if
contains the disk algebra, then there is
with
such that
is an automorphism of
and
on
.
AMS Subject Classifications:
Acknowledgements
The authors thank the referees for variable suggestions. They pointed out that in the paper [Möbius invariant function spaces, J. Reine Angew. Math. 363 (1985), 110–145], Arazy, Fisher and Peetre showed that if is a Möbius invariant function space and
for every
, then
. This is close to the subject of this paper, but does not directly relate to the one.
Notes
The first author is partially supported by Grant-in-Aid for Scientific Research, Japan Society for the Promotion of Science [grant number 24540164].