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 question formulated in the paper of Gromov, Henkin and Shubin [GHS] on holomorphic $L^{2}$ functions on coverings of pseudoconvex manifolds.