We analyze the structure of the space $\sigma\{M_p\}$ and $\sigma'\{M_p\}$. Under certain conditions on the matrix $\{C_{p,q}\exp(m_p(x))\}$ we investigate relations between the space $\sigma'\{M_p\}$ and some spaces of ultradistributions. Also we Investigate the Fourier transformation on the spaces $\sigma\{M_p\}$ and $\sigma'\{M_p\}$.