On the generalized Bessel potential and perfect functional completion

he class of generalized Bessel potentials is the main object study in this article. The potential a negative real power operator (I − Δγ), where Δγ = (...)∂xk - Laplace operator, γ (γ1,...,γn) multi-index consisting positive fixed numbers. When solving various problems for differential equations, proving embedding theorems some classes functions, and inverting integral operators, there need to consider functions up small, from point view problem under consideration, set. Often set Lebesgue measure zero taken as such small However, often sets turn out be too large neglected. For example, when boundary problem, behavior solution on essential. In regard, was construct complete admissible suitable specific problems. N. Aronshine K. Smith presented two stages constructing functional completion. first these finding exceptional sets. second find defined modulo that attached get class. It turns can infinitely many particular but each them corresponds essentially one clear most completion whose smallest, since then will with best possible accuracy. Whenever minimal exists, corresponding called perfect paper, completions are constructed norm associated kernel potential.