On the comparison of translation invariant convex differentiation bases

Pub Date : 2024-01-01 DOI:10.1515/gmj-2023-2070

Irakli Japaridze

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引用次数: 0

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.

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关于平移不变凸微分基的比较

众所周知，如果 B 和 B ′ {B^{/prime}} 是平移不变的凸密度微分基，并且与它们相关的最大算子在局部上相互大化，那么 B 和 B ′ {B^{/prime} 就微分同一类非负函数的积分。我们证明，在同样的条件下，鉴于 B 和 B ′ {B^{prime} 的正等价性，不可能断言它们的微分性质有更多的相似性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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