沃尔什-傅里叶级数的 Fejér 均值的一些新的弱-( $$H_{p}-L_p$$ ) 型不等式

IF 0.6 3区数学 Q3 MATHEMATICS Acta Mathematica Hungarica Pub Date : 2023-12-13 DOI:10.1007/s10474-023-01384-w

D. Baramidze, G. Tephnadze

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引用次数: 0

摘要

引入了Walsh-Fourier级数的fejsamr均值的一些新的加权极大算子。我们证明了对于某些“最优”权值，这些新算子从鞅Hardy空间$H_{p}(G)$有界到空间$\text{weak-}L_{p}(G)$，对于$0<p<1/2$。此外，我们还证明了该结果的锐度。因此，我们得到了一些新的和众所周知的结果。

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Some New weak-($H_{p}-L_p$) Type Inequalities For Weighted Maximal Operators Of Fejér Means Of Walsh–Fourier Series

We introduce some new weighted maximal operators of the Fejér means of the Walsh–Fourier series. We prove that for some "optimal" weights these new operators are bounded from the martingale Hardy space $H_{p}(G)$ to the space $\text{weak-}L_{p}(G)$ , for $0<p<1/2$. Moreover, we also prove sharpness of this result. As a consequence we obtain some new and well-known results.

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来源期刊

Acta Mathematica Hungarica 数学-数学

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

4-8 weeks

期刊介绍： Acta Mathematica Hungarica is devoted to publishing research articles of top quality in all areas of pure and applied mathematics as well as in theoretical computer science. The journal is published yearly in three volumes (two issues per volume, in total 6 issues) in both print and electronic formats. Acta Mathematica Hungarica (formerly Acta Mathematica Academiae Scientiarum Hungaricae) was founded in 1950 by the Hungarian Academy of Sciences.