关于 $A_p$ 条件的非标准表征

arXiv - MATH - Classical Analysis and ODEs Pub Date : 2024-09-12 DOI:arxiv-2409.07781

Andrei K. Lerner

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引用次数: 0

摘要

经典的穆肯霍普特 $A_p$ 条件是最大算子 $M$ 在 $L^p(w)$ 空间上有界的必要条件和充分条件。在本文中，我们得到了 $A_p$ 条件的另一个特征。因此，我们证明了当且仅当 $w\in A_p$ 时，加权 $L^p(w)$ Coifman--Fefferman 和 Fefferman--Stein 不等式的某些强版本成立。我们还给出了巴拿赫函数空间 $X$ 的新例子，使得 $M$ 在 $X$ 上有界，但在关联空间 $X'$ 上无界。

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On a non-standard characterization of the $A_p$ condition

The classical Muckenhoupt's $A_p$ condition is necessary and sufficient for the boundedness of the maximal operator $M$ on $L^p(w)$ spaces. In this paper we obtain another characterization of the $A_p$ condition. As a result, we show that some strong versions of the weighted $L^p(w)$ Coifman--Fefferman and Fefferman--Stein inequalities hold if and only if $w\in A_p$. We also give new examples of Banach function spaces $X$ such that $M$ is bounded on $X$ but not bounded on the associate space $X'$.

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arXiv - MATH - Classical Analysis and ODEs

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