Mathematics

2006, No. 2

V.A. Alyakin, D.E. Klepnev

THE DIAGONAL SEQUENCES OF MEASURES

A new notion of diagonality of sequence of measures is introduced. It is shown that the diagonality of measures implies the diagonality of its full variations. The sufficient conditions of uniform absolute continuity for two sequences of measures are obtained.

V.B. Dmitriev

A NON-LOCAL PROBLEM WITH INTEGRAL CONDITIONS FOR A WAVE EQUATION

Non-local problem with integral condition for the hyperbolic equation with n space variables is considered. The existence of the unique generalized solution is proved.

K.V. Lyckov

EXTRAPOLATION IN THE L_p SCALE AND CONVERGENCE OF ORTHOGONAL SERIES IN THE MARCINKEWICH SPACES

In the paper the extrapolation in the L_p scale is considered. Some new relations between norms in the class of symmetric (rearrangement invariant) spaces are presented. Applications to convergence of orthogonal series are given.