We prove an analog of the classical Hartogs extension theorem for certain (possibly unbounded) domains on coverings of strongly pseudoconvex manifolds. Our result is related to a problem posed in the paper of Gromov, Henkin and Shubin [GHS] on holomorphic L2 functions on coverings of pseudoconvex manifolds. Previously in [Br3] similar results were established for some domains on coverings of St...

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In this paper we answer an important question posed in the paper [GHS] by Gromov, Henkin and Shubin on existence of sufficiently many holomorphic L2 functions on arbitrary coverings of strongly pseudoconvex manifolds.