Structure functions of deep inelastic scattering and $e^+e^-$ annihilation at small x in QCD

A study is made of the behavior of the structure functions of deep inelastic scattering and $e^+e^-$-annihilation at small x in different asymptotic regimes. It is shown that when allowance is made for only the leading logarithms the Gribov–Lipatov relation between these functions holds in the Bjorkea regime $(Q^2\rightarrow\infty, x\rightarrow 0)$ and is violated in the Regge regime $(Q^2=\mathrm{const}, x\rightarrow 0)$. When the nonleading contributions are taken into account it also ceases to hold in the Bjorken regime.