BILATERAL SCALES OF HARDY INEQUALITIES AND THEIR APPLICATIONS TO SOME PROBLEMS OF MATHEMATICAL PHYSICS

摘要

In this paper, we study some problems of classical mathematical physics in the whole Euclidean space. It is well known that in this case studies of differential equations in the scale of Sobolev spaces meet an obstacle, namely, lack of the Poincare factorization inequality. We overcome this obstacle in the framework of Friedrichs-type factorization inequalities, choosing mean values of the functions on a certain sphere of fixed radius as the factorization parameter.