On the Possible Values of Upper and Lower Derivatives with Respect to Differentiation Bases of Product Structure

摘要

A solution of the Guzman's problem on possible values of upper and lower derivatives is given for the class of translation invariant and product type differentiation bases formed by n-dimensional intervals. Namely, the bases from the mentioned class are characterized, for which integral means of a summable function can boundedly diverge only on a set of zero measure.