The stability in $\ell$ of some difference schemes for heat conductivity equation

In the present paper, the stability in $\ell_p$ space for a wide class of difference schemes corresponding to the heat conductivity equation with variable coefficients is proved. This paper is the sequel of the author's previous works. The attraction of this methodology consists in that a prior estimations in $\ell_p$ for difference problems are obtained in the same way as in the case of initial differential problems in $L_p$ space.