From the integral estimates of functions to uniform. II. Exact estimates

Exact pointwise estimates of the functions under certain integral constraints on their growth are not often met in the theory of functions of complex variables. An example of this kind of estimation is the pointwise estimation of the module of function in the Fock space by integral norm of this function. We present functional-analytic scheme for obtaining such estimates and illustrate it on the examples of classical Fock–Bargman-type and Bergman–Djrbashian-type spaces of holomorphic functions on $n$-dimensional complex spaces, balls, polydiscs etc.