Závoti (2002) presented the mathematical description of the interpolation method especially for modeling the orbit of artificial satellites, which is suitable for approaching only certain 9 points. The task in this form stems from Grafarend and Schaffrin's (1993) study. During the time passed since the elaboration of the method, the generalization of the algorithm became necessary in the case when we have an arbitrary amount of measurement points, which must be approached according to a certain principle. The generalized method was successfully applied for modeling geodynamical processes, for describing the motion of the Earth's poles and for analyzing economical time series.
Several interpolation theorems on martingale Hardy spaces over weighted measure spaces are given. Our proofs are based on
the atomic decomposition of martingale Hardy spaces over weighted measure spaces. As applications of interpolation theorems,
some inequalities of martingale transform operator are obtained.
In this paper we define a new class of quartic splines of classC2 and solve the problem of (0, 2) interpolation by the elements of this class. We also study the possibility of the solution of the problems of (0, 1) and (1, 2) interpolations by the elements of the same class. Error estimates are obtained in each case.