鞅Hardy空间中二维Walsh-Fourier级数的尖锐强收敛结果

IF 1.4 3区数学 Q1 MATHEMATICS

Analysis and Mathematical Physics Pub Date : 2025-05-19 DOI:10.1007/s13324-025-01087-1

G. Tephnadze

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引用次数: 0

摘要

1996年，Weisz研究了二维Walsh-Fourier级数在鞅Hardy空间中的部分和\(S_{m,n}\)的强收敛性，但在\(2^{-\alpha }<m/n\le 2^{\alpha }\)。本文研究了二维Walsh-Fourier级数在鞅Hardy空间\({H_p^{\square }\left( G^2\right) }\) （\(0<p<1,\)）中不受指标限制的强收敛性。此外，我们还证明了我们的结果的锐性。

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Sharp strong convergence result of the two-dimensional Walsh-Fourier series in martingale Hardy spaces

In [55] Weisz investigated strong convergence of partial sums \(S_{m,n}\) of the two-dimensional Walsh-Fourier series in the martingale Hardy spaces, but under the condition when \(2^{-\alpha }<m/n\le 2^{\alpha }\). In this paper we investigate strong convergence of the two-dimensional Walsh-Fourier series in the martingale Hardy spaces \({H_p^{\square }\left( G^2\right) }\) for \(0<p<1,\) without any restriction on the indices. Moreover, we also prove sharpness of our result.

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来源期刊

Analysis and Mathematical Physics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.70

自引率

0.00%

发文量

122

期刊介绍： Analysis and Mathematical Physics (AMP) publishes current research results as well as selected high-quality survey articles in real, complex, harmonic; and geometric analysis originating and or having applications in mathematical physics. The journal promotes dialog among specialists in these areas.