傅立叶分析中马丁格尔-哈代-奥利奇-洛伦兹-卡拉马塔理论的应用

IF 1.1 2区 数学 Q1 MATHEMATICS
Zhiwei Hao, Libo Li, Ferenc Weisz
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引用次数: 0

摘要

在这篇文章中,我们讨论了马氏哈代-奥利茨-洛伦茨-卡拉马塔空间在傅里叶分析中的应用。更确切地说,我们证明了如果 \(f\in L_{Phi ,q,b}\) with \(1<p_-\le p_+<\infty \),沃尔什-傅里叶级数的偏和收敛于函数的规范。介绍了马氏哈代奥利茨-洛伦茨-卡拉马塔空间上最大算子的等价性。我们还研究了 Fejér 可求和方法,并证明了最大 Fejér 算子从鞅 Hardy Orlicz-Lorentz-Karamata 空间到 Orlicz-Lorentz-Karamata 空间是有界的。因此,我们得到了关于费杰尔手段几乎无处收敛和规范收敛的结论。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Applications of martingale Hardy Orlicz–Lorentz–Karamata theory in Fourier analysis

In this article, we discuss the applications of martingale Hardy Orlicz–Lorentz–Karamata spaces in Fourier analysis. More precisely, we show that the partial sums of the Walsh–Fourier series converge to the function in norm if \(f\in L_{\Phi ,q,b}\) with \(1<p_-\le p_+<\infty \). The equivalence of maximal operators on martingale Hardy Orlicz–Lorentz–Karamata spaces is presented. The Fejér summability method is also studied and it is proved that the maximal Fejér operator is bounded from martingale Hardy Orlicz–Lorentz–Karamata spaces to Orlicz–Lorentz–Karamata spaces. As a consequence, we obtain conclusions about almost everywhere and norm convergence of Fejér means.

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来源期刊
CiteScore
2.00
自引率
8.30%
发文量
67
审稿时长
>12 weeks
期刊介绍: The Banach Journal of Mathematical Analysis (Banach J. Math. Anal.) is published by Birkhäuser on behalf of the Tusi Mathematical Research Group. Banach J. Math. Anal. is a peer-reviewed electronic journal publishing papers of high standards with deep results, new ideas, profound impact, and significant implications in all areas of functional analysis and operator theory and all modern related topics. Banach J. Math. Anal. normally publishes survey articles and original research papers numbering 15 pages or more in the journal’s style. Shorter papers may be submitted to the Annals of Functional Analysis or Advances in Operator Theory.
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