Some characterizations of Bloch functions on strongly pseudoconvex domains (Q1346797)

This paper contains 3 characterisations of Bloch functions on smoothly bounded, strongly pseudoconvex domains in terms of invariant geometry, Bergman-Carleson measures and certain invariant random processes, respectively. This involves extending and modifying earlier work by \textit{J. Choa}, \textit{H. Kim} and \textit{Y. Park} [Bull. Korean Math. Soc. 29, No. 2, 285-293 (1992; Zbl 0761.32004), \textit{K. Muramoto} [Math. J. Toyama Univ. 13, 45-50 (1990; Zbl 0741.60034)], and \textit{T. J. Lyons} [Bull. Lond. Math. Soc. 22, No. 2, 159-162 (1990; Zbl 0708.32033)]. The main result is applied to prove a multidimensional generalisation of Lyons' law of the iterated logarithm.