The AdS/CFT correspondence formulated by Juan Maldacena has inspired the construction of numerous models in the theory of strong interactions, condensed matter physics and some other areas where the problem of strong coupling arises. The AdS/CFT correspondence hypothesis states, in particular, that 4-dimensional CFT in flat space in the strong-coupling regime can be described in terms of the dual theory of gravity in AdS5 space. This hypothesis has been well tested only in the so-called strong formulation when the bulk is AdS5 space. In this paper, an attempt is made to analyze the modifications of the AdS/CFT matching recipes, outside the strong hypothesis.
To this end, a method for directly shifting the cutoff boundary to the UV region for the AdS/CFT correspondence is constructed and a modification of the bulk-normalized solutions of the zero mode of the dilaton field on the space AdS5(mod) is proposed, which arises as a result of taking into account the second order of smallness of r/R in the metric created by the stack D3 -branes in type IIB supergravity. A direct factorization of corrections to the solution against the background of AdS5 is performed. For the obtained corrections, the equation of motion, recipes for modifying the bulk-bulk and bulk-boundary propagators, as well as the correlator of two primary operators corresponding to the Lagrangian N=4 SYM, are obtained. It is also shown how this construction can be related to the correction in terms of the t'Hooft constant in the dual gauge theory.