Elements of DX s Mp. and DX s Mp4 as Boundary Values of L L Holomorphic Functions

We give representations of elements belonging to DLX sMp. and DLX sMp4, sg 1, `., where Mp is a non-quasianalytic sequence, as boundary values of holomorphic functions which satisfy appropriate estimates on the boundary of their domains. Conversely, we prove that the same estimates on holomorphic functions imply their DX s Mp.- and DX s L L Mp4-boundary values. With the stronger assumptions on Mp we obtain that appropriate L`, resp. L1, estimates on holomorphic functions imply their boundary values in DX ` Mp. and DX ` Mp4, resp. DX Mp. and DX Mp4L L L1 L1 .