Affiliation:
1. Akaki Tsereteli State University , 59 Tamar Mepe Str. , Kutaisi 4600 , Georgia
Abstract
Abstract
It is known that if B and
B
′
{B^{\prime}}
are translation invariant convex density differentiation bases and the maximal operators associated to them locally majorize each other, then B and
B
′
{B^{\prime}}
differentiate the integrals of the same class of non-negative functions. We show that under the same conditions it is not possible to assert more about similarity of the differential properties of B and
B
′
{B^{\prime}}
in view of their positive equivalence.