Gegenbauer微分算子卷积的O’Neil不等式及其应用

IF 0.8 4区数学

数学研究 Pub Date : 2020-06-01 DOI:10.4208/jms.v53n1.20.05

Vagif S. Guliyev sci

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引用次数: 1

摘要

本文证明了与Gegenbauer微分算子Gλ相关的卷积算子（G-卷积）的一个O’Neil不等式。通过对重排使用O’Neil不等式，我们得到了G-卷积的逐点重排估计。作为一个应用，我们得到了从空间Lp，λ到Lq，λ和从空间L1，λ到弱空间WLp，λ的G-分式极大算子和G-分式积分算子的参数有界性的充要条件。AMS科目分类：42B20、42B25、42B35、47G10、47B37

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O'Neil Inequality for Convolutions Associated with Gegenbauer Differential Operator and some Applications

In this paper we prove an O’Neil inequality for the convolution operator (G-convolution) associated with the Gegenbauer differential operator Gλ. By using an O’Neil inequality for rearrangements we obtain a pointwise rearrangement estimate of the G-convolution. As an application, we obtain necessary and sufficient conditions on the parameters for the boundedness of the G-fractional maximal and G-fractional integral operators from the spaces Lp,λ to Lq,λ and from the spaces L1,λ to the weak spaces WLp,λ. AMS subject classifications: 42B20, 42B25, 42B35, 47G10, 47B37

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来源期刊

数学研究 MATHEMATICS-

自引率

0.00%

发文量

1109

期刊介绍： Journal of Mathematical Study (JMS) is a comprehensive mathematical journal published jointly by Global Science Press and Xiamen University. It publishes original research and survey papers, in English, of high scientific value in all major fields of mathematics, including pure mathematics, applied mathematics, operational research, and computational mathematics.