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On the comparison of translation invariant convex differentiation bases

  • Irakli Japaridze EMAIL logo
Published/Copyright: January 2, 2024
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Abstract

It is known that if B and B are translation invariant convex density differentiation bases and the maximal operators associated to them locally majorize each other, then B and B 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 in view of their positive equivalence.

MSC 2020: 28A15; 42B25

Dedicated to the memory of Tamaz Zerekidze


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Received: 2023-02-14
Revised: 2023-05-13
Accepted: 2023-05-18
Published Online: 2024-01-02
Published in Print: 2024-04-01

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