Some new restricted maximal operators of Fejér means of Walsh–Fourier series

IF 1.1 2区数学 Q1 MATHEMATICS

Banach Journal of Mathematical Analysis Pub Date : 2023-09-12 DOI:10.1007/s43037-023-00300-2

Davit Baramidze, Lasha Baramidze, Lars-Erik Perssson, George Tephnadze

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引用次数: 0

Abstract

Abstract In this paper, we derive the maximal subspace of natural numbers $$\left\{ n_{k}:k\ge 0\right\} ,$$ n k : k ≥ 0 , such that the restricted maximal operator, defined by $${\sup }_{k\in {\mathbb {N}}}\left| \sigma _{n_{k}}F\right| $$ sup k ∈ N σ n k F on this subspace of Fejér means of Walsh–Fourier series is bounded from the martingale Hardy space $$H_{1/2}$$ H 1 / 2 to the Lebesgue space $$L_{1/2}.$$ L 1 / 2 . The sharpness of this result is also proved.

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沃尔什-傅里叶级数fejsamr均值的一些新的限制极大算子

摘要本文导出了自然数的极大子空间$$\left\{ n_{k}:k\ge 0\right\} ,$$ n k: k≥0，使得约束极大算子(由$${\sup }_{k\in {\mathbb {N}}}\left| \sigma _{n_{k}}F\right| $$ sup k∈n σ n k F定义)在这个w -傅里叶级数的fej均值子空间上由鞅Hardy空间$$H_{1/2}$$ H 1 / 2有界到Lebesgue空间$$L_{1/2}.$$ L 1 / 2。并证明了该结果的清晰性。

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来源期刊

Banach Journal of Mathematical Analysis 数学-数学

CiteScore

2.00

自引率

8.30%

发文量

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.