For a regularly converging-in-C series A(z)=?n=1?anf(?nz), where f is an entire transcendental function, the asymptotic behavior of function Mf?1(MA(r)), Mf(r)=max{|f(z)|:|z|=r}, investigated. It proven that, under certain conditions on functions f, ?, and coefficients an, equality limr?+??(Mf?1(MA(r)))?(r)=1 correct. A similar result obtained for Laplace–Stiltjes-type integral I(r)=?0?a(x)f(rx...

In this paper we prove Liouville type theorem for the stationary Navier–Stokes equations in \(\mathbb {R}^3\) under assumptions on relative decays of velocity, pressure and head pressure. More precisely, show that any smooth solution (u, p) satisfying \(u(x) \rightarrow 0\) as \(|x|\rightarrow +\infty \) condition finite Dirichlet integral \(\int _{\mathbb {R}^3} | \nabla u|^2 dx <+\infty is tr...