On the Differentiation of Integrals of Functions From Orlicz Classes

This paper is a direct continuation of [4]. The study of conditions on a basis which ensure that it differentiate Φ(L) (Rⁿ) is a central problem of the theory of differentiation of integrals. There are many papers (see [1]) devoted to the study of connections between the differentiation of various function classes on the one hand, and the halo and covering properties and estimates for the maximal operators on the other. However, the problem whether there exist at all bases which differentiate various classes Φ(L)(Rⁿ) has not been much discussed. In the present paper we prove the existence of bases which differentiate precisely a given class Φ(L) (Rⁿ), with natural restrictions on Φ. The analogous question for bases of rectangles is also considered.