Abstract. We establish the topological reflexivity of several spaces of analytic functions for which characterizations of their respective isometry groups are available. Namely, we consider the following spaces of analytic functions: the Novinger--Oberlin spaces consisting of those functions on the disk with the property that $f'\in H_p$ and also the more general Kolaski spaces; the Ida--Mochizuki spaces consisting of functions on the disk such that $$\sup_{0 < r < 1}\int_{\rm T}\log{(1 + |f(r\xi )|})^p d\sigma(\xi )< \infty $$ (with $p \geq1$, ${\rm T}$ is the unit circle and $d\sigma $ denotes Lebesgue measure); the subspace of the Nevanlinna class in several variables, known as the Smirnov Class, consisting of holomorphic functions $f$ on $X$ ($X$ the unit ball or the polydisk in $C^n$) so that $$\sup_{0\leq r< 1} \int_{\partial X} \log ^+(|f(rz)|) d\sigma(z) =\int_{\partial X} \log ^+(|f(z)|) d\sigma(z) < \infty.$$

AMS Subject Classification (1991): 30D55; 30D05

Keyword(s): isometries, local surjective isometries, algebraically reflexive Banach spaces, topologically reflexive Banach spaces

Received December 18, 2007, and in revised form December 15, 2008. (Registered under 6062/2009.)