**On Representation of Functions
from the Space **ReH_{1}

In the article it is considered the question
of representation of elements from the space ReH_{1} by
functional series with absolutely convergent coefficients. Using the fact that
the space BMO is conjugate to ReH_{1}, Ch.
Fefferman's theorem is strengthened, and it is shown that the functions which
participate in the representation can't be generated by shifts and dilations of
any function.