Copyright © 2009 Stevo Stević and Sei-Ichiro Ueki. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We introduce a new space consisting of all holomorphic functions on the unit ball such that , where , ( is the normalized Lebesgue volume measure on , and is a normalization constant, that is, ), and for . Some basic properties of this space are presented. Among other results we proved that with the metric is an -algebra with respect to pointwise addition and multiplication. We also prove that every linear isometry of into itself has the form for some such that and some which is a holomorphic self-map of satisfying a measure-preserving property with respect to the measure . As a consequence of this result we obtain a complete characterization of all linear bijective isometries of .