A characterization of two-weight norm inequalities for multidimensional Hausdorff operators on Lebesgue spaces

IF 0.8 3区数学 Q2 MATHEMATICS

Positivity Pub Date : 2024-02-21 DOI:10.1007/s11117-024-01031-w

Rovshan Bandaliyev, Dunya Aliyeva

引用次数: 0

Abstract

In this paper we give necessary and sufficient conditions for the boundedness of the multidimensional Hausdorff operator on weighted Lebesgue spaces. In particular, we establish necessary and sufficient conditions for the boundedness of special type of the multidimensional Hausdorff operator on weighted Lebesgue spaces for monotone radial weight functions. Also, we get similar results for important operators of harmonic analysis which are special cases of the multidimensional Hausdorff operator. The results are illustrated by a number of examples.

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Lebesgue 空间上多维 Hausdorff 算子的二重规范不等式的表征

本文给出了加权 Lebesgue 空间上多维 Hausdorff 算子有界性的必要和充分条件。特别是，我们为单调径向权重函数的加权 Lebesgue 空间上多维 Hausdorff 算子特殊类型的有界性建立了必要和充分条件。此外，我们还得到了谐波分析中重要算子的类似结果，这些算子是多维豪斯多夫算子的特例。我们通过一些例子来说明这些结果。

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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来源期刊

Positivity 数学-数学

CiteScore

1.80

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： The purpose of Positivity is to provide an outlet for high quality original research in all areas of analysis and its applications to other disciplines having a clear and substantive link to the general theme of positivity. Specifically, articles that illustrate applications of positivity to other disciplines - including but not limited to - economics, engineering, life sciences, physics and statistical decision theory are welcome. The scope of Positivity is to publish original papers in all areas of mathematics and its applications that are influenced by positivity concepts.