Hardy and Bergman spaces on hyperconvex domains and their composition operators Evgeny PoletskyM. Stessin 32F0532E2532E20plurisubharmonic functionspluripotential theorycomposition operators We introduce the scale of weighted Bergman spaces on hyperconvex domains in $\mathbb{C}^n$ and use the Lelong-Jensen formula to prove some fundamental results about these spaces. In particular, generalizations of such classical results as the Littlewood subordination principle, the Littlewood-Paley identity and the change of variables formula are proven. Geometric properties of the introduced norms are revealed by the Nevanlinna counting function associated with a chosen exhaustion. In the last several sections we prove boundedness and compactness results for composition operators generated by holomorphic mappings of hyperconvex domains. Indiana University Mathematics Journal 2008 text pdf 10.1512/iumj.2008.57.3360 10.1512/iumj.2008.57.3360 en Indiana Univ. Math. J. 57 (2008) 2153 - 2202 state-of-the-art mathematics http://iumj.org/access/