Hartogs Type Theorems for CR L^{2} functions on Coverings of Strongly Pseudoconvex Manifolds

Abstract

We prove an analog of the classical Hartogs extension theorem for CR $L^2$ functions defined on boundaries of 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 $L_2$ functions on coverings of pseudoconvex manifolds.

16 pages, revised version