In this work, a space Hilbert problem is solved, with the boundary condition set on the boundary of the unlimited full bicircular region of class (T^∞) or on the boundary of the region D_pq={z∈C²: |z₁|^p|z₂|^q<1; p,q∈N}. The main devices used for solving the space Hilbert problem are Temlyakov integrals of second kind.