Armen A. Vagharshakyan

On Representation of Functions from the Space ReH1

   In the article it is considered the question of representation of elements from the space ReH1 by functional series with absolutely convergent coefficients. Using the fact that the space BMO is conjugate to ReH1, 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.