An equivalent integral norm in a dual space

In the present paper, the problem of describing a dual space in terms of the Hilbert transform is considered. We establish the necessary and sufficient conditions for the space $\widetilde B_2(G,\mu)$ to possess an integral norm equivalent to the initial one. We find the form of this norm. Using the general result of this work, we specify the recent result of the author and R. S. Yulmukhametov. The method suggested in the paper is based on the theory of orthosimilar systems. This method can be used to solve the problem of describing a dual space in terms of the Fourier–Lapalace transform and in terms of others complete system of functions.