The Chover-type law of the iterated logarithm for certain power series

Let {p(n), n >= 0} be a sequence of real numbers with p(n) similar to R(n), R((.)) a regular varying function with index greater than -1/alpha (0 < alpha < 2). We prove the Chover-type law of the iterated logarithm for the (J(p)) power transform of sequence {X-n, n >= 0} of independent identically distributed stable random variables with exponent alpha.