On Hartogs extension theorems for separately (⋅, W)-holomorphic functions

Abstract

In this paper, we study the holomorphic extension of separately (⋅, W)-holomorphic functions from a product of a [Formula: see text]-regular compact subset in a Stein space with a Stein space to some its neighborhood. At the same time, we generalize the Siciak's result to separately (⋅, W)-holomorphic functions with pluripolar singularities on the crosses.