Boundary conditions for the photon structure function in the leading and subleading order

The importance of boundary conditions (at $Q^2={Q_0}^2$) inherent in any general solution of the inhomogeneous photon evolution equations is stressed. Their inclusion is crucial at present energies, especially in connection with investigations concerning the relative importance of subleading corrections at small values of the scaling variable $x$. The framework for a direct $x$-variable analysis is formulated explicitly.