From Integral Estimates of Functions to Uniform Ones. II. Sharp Versions

In the theory of functions of complex variables, exact pointwise estimates of the functions, obtained under certain integral constraints on their growth, are not common. As an example of such estimates, we can mention the pointwise estimation of the module of a function from the Fock space by its integral norm. Here we present a functional-analytic scheme for obtaining such estimates and illustrate it on the examples of the classical Fock–Bargman and Bergman–Djrbashian type spaces of holomorphic functions defined on the n-dimensional complex space, balls, polydiscs, etc.