  We establish bounds for the covariance of a large class of functions of
infinite variance stable random variables, including unbounded functions such
as the power function and the logarithm. These bounds involve measures of
dependence between the stable variables, some of which are new. The bounds are
also used to deduce the central limit theorem for unbounded functions of stable
moving average time series. This result extends the earlier results of Tailen
Hsing and the authors on central limit theorems for bounded functions of stable
moving averages. It can be used to show asymptotic normality of wavelet-based
estimators of the self-similarity parameter in fractional stable motions.
